Issolvi sqrt{3/5}(x+1)+sqrt{5/3}(x-1)=1/15

$$\sqrt { \frac { 3 } { 5 } } ( x + 1 ) + \sqrt { \frac { 5 } { 3 } } ( x - 1 ) = \frac { 1 } { 15 }$$

Solvi għal x

$$x=\frac{\sqrt{15}+30}{120}\approx 0.282274861$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{3}{5}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{3}}{\sqrt{5}}.

$$\frac{\sqrt{3}}{\sqrt{5}}\left(x+1\right)+\sqrt{\frac{5}{3}}\left(x-1\right)=\frac{1}{15}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{3}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(x+1\right)+\sqrt{\frac{5}{3}}\left(x-1\right)=\frac{1}{15}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{\sqrt{3}\sqrt{5}}{5}\left(x+1\right)+\sqrt{\frac{5}{3}}\left(x-1\right)=\frac{1}{15}$$

Biex timmultiplika \sqrt{3} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{15}}{5}\left(x+1\right)+\sqrt{\frac{5}{3}}\left(x-1\right)=\frac{1}{15}$$

Esprimi \frac{\sqrt{15}}{5}\left(x+1\right) bħala frazzjoni waħda.

$$\frac{\sqrt{15}\left(x+1\right)}{5}+\sqrt{\frac{5}{3}}\left(x-1\right)=\frac{1}{15}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{5}{3}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{5}}{\sqrt{3}}.

$$\frac{\sqrt{15}\left(x+1\right)}{5}+\frac{\sqrt{5}}{\sqrt{3}}\left(x-1\right)=\frac{1}{15}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{5}}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{\sqrt{15}\left(x+1\right)}{5}+\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\left(x-1\right)=\frac{1}{15}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{\sqrt{15}\left(x+1\right)}{5}+\frac{\sqrt{5}\sqrt{3}}{3}\left(x-1\right)=\frac{1}{15}$$

Biex timmultiplika \sqrt{5} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{15}\left(x+1\right)}{5}+\frac{\sqrt{15}}{3}\left(x-1\right)=\frac{1}{15}$$

Esprimi \frac{\sqrt{15}}{3}\left(x-1\right) bħala frazzjoni waħda.

$$\frac{\sqrt{15}\left(x+1\right)}{5}+\frac{\sqrt{15}\left(x-1\right)}{3}=\frac{1}{15}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 5 u 3 huwa 15. Immultiplika \frac{\sqrt{15}\left(x+1\right)}{5} b'\frac{3}{3}. Immultiplika \frac{\sqrt{15}\left(x-1\right)}{3} b'\frac{5}{5}.

$$\frac{3\sqrt{15}\left(x+1\right)}{15}+\frac{5\sqrt{15}\left(x-1\right)}{15}=\frac{1}{15}$$

Billi \frac{3\sqrt{15}\left(x+1\right)}{15} u \frac{5\sqrt{15}\left(x-1\right)}{15} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{3\sqrt{15}\left(x+1\right)+5\sqrt{15}\left(x-1\right)}{15}=\frac{1}{15}$$

Agħmel il-multiplikazzjonijiet fi 3\sqrt{15}\left(x+1\right)+5\sqrt{15}\left(x-1\right).

$$\frac{3\sqrt{15}x+3\sqrt{15}+5\sqrt{15}x-5\sqrt{15}}{15}=\frac{1}{15}$$

Ikkombina termini simili f'3\sqrt{15}x+3\sqrt{15}+5\sqrt{15}x-5\sqrt{15}.

$$\frac{8\sqrt{15}x-2\sqrt{15}}{15}=\frac{1}{15}$$

Immultiplika ż-żewġ naħat b'15.

$$8\sqrt{15}x-2\sqrt{15}=\frac{1}{15}\times 15$$

Annulla 15 u 15.

$$8\sqrt{15}x-2\sqrt{15}=1$$

Żid 2\sqrt{15} maż-żewġ naħat.

$$8\sqrt{15}x=1+2\sqrt{15}$$

L-ekwazzjoni hija f'forma standard.

$$8\sqrt{15}x=2\sqrt{15}+1$$

Iddividi ż-żewġ naħat b'8\sqrt{15}.

$$\frac{8\sqrt{15}x}{8\sqrt{15}}=\frac{2\sqrt{15}+1}{8\sqrt{15}}$$

Meta tiddividi b'8\sqrt{15} titneħħa l-multiplikazzjoni b'8\sqrt{15}.

$$x=\frac{2\sqrt{15}+1}{8\sqrt{15}}$$

Iddividi 1+2\sqrt{15} b'8\sqrt{15}.

$$x=\frac{\sqrt{15}}{120}+\frac{1}{4}$$