Issolvi {left(10/3right)}^2+{left(frac{2sqrt{73}}{3}right)}^2=2{left(frac{sqrt{52}}{3}right)}^2+2x^2

$${ \left( \frac{ 10 }{ 3 } \right) }^{ 2 } + { \left( \frac{ 2 \sqrt{ 73 } }{ 3 } \right) }^{ 2 } =2 { \left( \frac{ \sqrt{ 52 } }{ 3 } \right) }^{ 2 } +2 { x }^{ 2 }$$

Solvi għal x

$$x=4$$

$$x=-4$$

Passi li Jużaw id-Differenza tal-Kwadrati

Ikkalkula \frac{10}{3} bil-power ta' 2 u tikseb \frac{100}{9}.

$$\frac{100}{9}+\left(\frac{2\sqrt{73}}{3}\right)^{2}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Biex tgħolli \frac{2\sqrt{73}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{100}{9}+\frac{\left(2\sqrt{73}\right)^{2}}{3^{2}}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Espandi 3^{2}.

$$\frac{100}{9}+\frac{\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Billi \frac{100}{9} u \frac{\left(2\sqrt{73}\right)^{2}}{9} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Iffattura 52=2^{2}\times 13. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 13} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{13}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{2\sqrt{13}}{3}\right)^{2}+2x^{2}$$

Biex tgħolli \frac{2\sqrt{13}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \frac{\left(2\sqrt{13}\right)^{2}}{3^{2}}+2x^{2}$$

Esprimi 2\times \frac{\left(2\sqrt{13}\right)^{2}}{3^{2}} bħala frazzjoni waħda.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}}+2x^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2x^{2} b'\frac{3^{2}}{3^{2}}.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}}+\frac{2x^{2}\times 3^{2}}{3^{2}}$$

Billi \frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}} u \frac{2x^{2}\times 3^{2}}{3^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Espandi \left(2\sqrt{73}\right)^{2}.

$$\frac{100+2^{2}\left(\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{100+4\left(\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Il-kwadrat ta' \sqrt{73} huwa 73.

$$\frac{100+4\times 73}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 4 u 73 biex tikseb 292.

$$\frac{100+292}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Żid 100 u 292 biex tikseb 392.

$$\frac{392}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Espandi \left(2\sqrt{13}\right)^{2}.

$$\frac{392}{9}=\frac{2\times 2^{2}\left(\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{392}{9}=\frac{2\times 4\left(\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Il-kwadrat ta' \sqrt{13} huwa 13.

$$\frac{392}{9}=\frac{2\times 4\times 13+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 4 u 13 biex tikseb 52.

$$\frac{392}{9}=\frac{2\times 52+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 2 u 52 biex tikseb 104.

$$\frac{392}{9}=\frac{104+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{392}{9}=\frac{104+2x^{2}\times 9}{3^{2}}$$

Immultiplika 2 u 9 biex tikseb 18.

$$\frac{392}{9}=\frac{104+18x^{2}}{3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{392}{9}=\frac{104+18x^{2}}{9}$$

Iddividi kull terminu ta' 104+18x^{2} b'9 biex tikseb\frac{104}{9}+2x^{2}.

$$\frac{392}{9}=\frac{104}{9}+2x^{2}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\frac{104}{9}+2x^{2}=\frac{392}{9}$$

Naqqas \frac{392}{9} miż-żewġ naħat.

$$\frac{104}{9}+2x^{2}-\frac{392}{9}=0$$

Naqqas \frac{392}{9} minn \frac{104}{9} biex tikseb -32.

$$-32+2x^{2}=0$$

Iddividi ż-żewġ naħat b'2.

$$-16+x^{2}=0$$

Ikkunsidra li -16+x^{2}. Erġa' ikteb -16+x^{2} bħala x^{2}-4^{2}. Id-differenza tal-kwadrati tista' tiġi fatturata billi tuża r-regola: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

Biex issib soluzzjonijiet tal-ekwazzjoni, solvi x-4=0 u x+4=0.

$$x=4 x=-4$$

Passi billi Ssib l-Għerq Kwadrat

Ikkalkula \frac{10}{3} bil-power ta' 2 u tikseb \frac{100}{9}.

$$\frac{100}{9}+\left(\frac{2\sqrt{73}}{3}\right)^{2}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Biex tgħolli \frac{2\sqrt{73}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{100}{9}+\frac{\left(2\sqrt{73}\right)^{2}}{3^{2}}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Espandi 3^{2}.

$$\frac{100}{9}+\frac{\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Billi \frac{100}{9} u \frac{\left(2\sqrt{73}\right)^{2}}{9} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Iffattura 52=2^{2}\times 13. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 13} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{13}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{2\sqrt{13}}{3}\right)^{2}+2x^{2}$$

Biex tgħolli \frac{2\sqrt{13}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \frac{\left(2\sqrt{13}\right)^{2}}{3^{2}}+2x^{2}$$

Esprimi 2\times \frac{\left(2\sqrt{13}\right)^{2}}{3^{2}} bħala frazzjoni waħda.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}}+2x^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2x^{2} b'\frac{3^{2}}{3^{2}}.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}}+\frac{2x^{2}\times 3^{2}}{3^{2}}$$

Billi \frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}} u \frac{2x^{2}\times 3^{2}}{3^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Espandi \left(2\sqrt{73}\right)^{2}.

$$\frac{100+2^{2}\left(\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{100+4\left(\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Il-kwadrat ta' \sqrt{73} huwa 73.

$$\frac{100+4\times 73}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 4 u 73 biex tikseb 292.

$$\frac{100+292}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Żid 100 u 292 biex tikseb 392.

$$\frac{392}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Espandi \left(2\sqrt{13}\right)^{2}.

$$\frac{392}{9}=\frac{2\times 2^{2}\left(\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{392}{9}=\frac{2\times 4\left(\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Il-kwadrat ta' \sqrt{13} huwa 13.

$$\frac{392}{9}=\frac{2\times 4\times 13+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 4 u 13 biex tikseb 52.

$$\frac{392}{9}=\frac{2\times 52+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 2 u 52 biex tikseb 104.

$$\frac{392}{9}=\frac{104+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{392}{9}=\frac{104+2x^{2}\times 9}{3^{2}}$$

Immultiplika 2 u 9 biex tikseb 18.

$$\frac{392}{9}=\frac{104+18x^{2}}{3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{392}{9}=\frac{104+18x^{2}}{9}$$

Iddividi kull terminu ta' 104+18x^{2} b'9 biex tikseb\frac{104}{9}+2x^{2}.

$$\frac{392}{9}=\frac{104}{9}+2x^{2}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\frac{104}{9}+2x^{2}=\frac{392}{9}$$

Naqqas \frac{104}{9} miż-żewġ naħat.

$$2x^{2}=\frac{392}{9}-\frac{104}{9}$$

Naqqas \frac{104}{9} minn \frac{392}{9} biex tikseb 32.

$$2x^{2}=32$$

Iddividi ż-żewġ naħat b'2.

$$x^{2}=\frac{32}{2}$$

Iddividi 32 b'2 biex tikseb16.

$$x^{2}=16$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$x=4 x=-4$$

Passi għall-Użu tal-Formula Kwadratika

Ikkalkula \frac{10}{3} bil-power ta' 2 u tikseb \frac{100}{9}.

$$\frac{100}{9}+\left(\frac{2\sqrt{73}}{3}\right)^{2}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Biex tgħolli \frac{2\sqrt{73}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{100}{9}+\frac{\left(2\sqrt{73}\right)^{2}}{3^{2}}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Espandi 3^{2}.

$$\frac{100}{9}+\frac{\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Billi \frac{100}{9} u \frac{\left(2\sqrt{73}\right)^{2}}{9} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{\sqrt{52}}{3}\right)^{2}+2x^{2}$$

Iffattura 52=2^{2}\times 13. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 13} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{13}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \left(\frac{2\sqrt{13}}{3}\right)^{2}+2x^{2}$$

Biex tgħolli \frac{2\sqrt{13}}{3} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=2\times \frac{\left(2\sqrt{13}\right)^{2}}{3^{2}}+2x^{2}$$

Esprimi 2\times \frac{\left(2\sqrt{13}\right)^{2}}{3^{2}} bħala frazzjoni waħda.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}}+2x^{2}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2x^{2} b'\frac{3^{2}}{3^{2}}.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}}+\frac{2x^{2}\times 3^{2}}{3^{2}}$$

Billi \frac{2\times \left(2\sqrt{13}\right)^{2}}{3^{2}} u \frac{2x^{2}\times 3^{2}}{3^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{100+\left(2\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Espandi \left(2\sqrt{73}\right)^{2}.

$$\frac{100+2^{2}\left(\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{100+4\left(\sqrt{73}\right)^{2}}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Il-kwadrat ta' \sqrt{73} huwa 73.

$$\frac{100+4\times 73}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 4 u 73 biex tikseb 292.

$$\frac{100+292}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Żid 100 u 292 biex tikseb 392.

$$\frac{392}{9}=\frac{2\times \left(2\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Espandi \left(2\sqrt{13}\right)^{2}.

$$\frac{392}{9}=\frac{2\times 2^{2}\left(\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{392}{9}=\frac{2\times 4\left(\sqrt{13}\right)^{2}+2x^{2}\times 3^{2}}{3^{2}}$$

Il-kwadrat ta' \sqrt{13} huwa 13.

$$\frac{392}{9}=\frac{2\times 4\times 13+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 4 u 13 biex tikseb 52.

$$\frac{392}{9}=\frac{2\times 52+2x^{2}\times 3^{2}}{3^{2}}$$

Immultiplika 2 u 52 biex tikseb 104.

$$\frac{392}{9}=\frac{104+2x^{2}\times 3^{2}}{3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{392}{9}=\frac{104+2x^{2}\times 9}{3^{2}}$$

Immultiplika 2 u 9 biex tikseb 18.

$$\frac{392}{9}=\frac{104+18x^{2}}{3^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{392}{9}=\frac{104+18x^{2}}{9}$$

Iddividi kull terminu ta' 104+18x^{2} b'9 biex tikseb\frac{104}{9}+2x^{2}.

$$\frac{392}{9}=\frac{104}{9}+2x^{2}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\frac{104}{9}+2x^{2}=\frac{392}{9}$$

Naqqas \frac{392}{9} miż-żewġ naħat.

$$\frac{104}{9}+2x^{2}-\frac{392}{9}=0$$

Naqqas \frac{392}{9} minn \frac{104}{9} biex tikseb -32.

$$-32+2x^{2}=0$$

Ekwazzjonijiet kwadratiċi bħal din, b'terminu x^{2} term iżda b'ebda terminu x, xorta jistgħu jiġu solvuti billi tuża l-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ladarba jitqiegħdu fil-forma standard: ax^{2}+bx+c=0.

$$2x^{2}-32=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 2 għal a, 0 għal b, u -32 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-32\right)}}{2\times 2}$$

Ikkwadra 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-32\right)}}{2\times 2}$$

Immultiplika -4 b'2.

$$x=\frac{0±\sqrt{-8\left(-32\right)}}{2\times 2}$$

Immultiplika -8 b'-32.

$$x=\frac{0±\sqrt{256}}{2\times 2}$$

Ħu l-għerq kwadrat ta' 256.

$$x=\frac{0±16}{2\times 2}$$

Immultiplika 2 b'2.

$$x=\frac{0±16}{4}$$

Issa solvi l-ekwazzjoni x=\frac{0±16}{4} fejn ± hija plus. Iddividi 16 b'4.

$$x=4$$

Issa solvi l-ekwazzjoni x=\frac{0±16}{4} fejn ± hija minus. Iddividi -16 b'4.

$$x=-4$$

L-ekwazzjoni issa solvuta.

$$x=4 x=-4$$