Issolvi B=frac{sqrt{2}-sqrt{7}}{5-sqrt{8}}

$$B = \frac { \sqrt { 2 } - \sqrt { 7 } } { 5 - \sqrt { 8 } }$$

Solvi għal B

$$B=\frac{5\sqrt{2}+4-2\sqrt{14}-5\sqrt{7}}{17}\approx -0.567117854$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$B=\frac{\sqrt{2}-\sqrt{7}}{5-2\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}-\sqrt{7}}{5-2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-5+2\sqrt{2}.

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{\left(5-2\sqrt{2}\right)\left(5+2\sqrt{2}\right)}$$

Ikkunsidra li \left(5-2\sqrt{2}\right)\left(5+2\sqrt{2}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{5^{2}-\left(-2\sqrt{2}\right)^{2}}$$

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{25-\left(-2\sqrt{2}\right)^{2}}$$

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

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{25-\left(-2\right)^{2}\left(\sqrt{2}\right)^{2}}$$

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

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{25-4\left(\sqrt{2}\right)^{2}}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{25-4\times 2}$$

Immultiplika 4 u 2 biex tikseb 8.

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{25-8}$$

Naqqas 8 minn 25 biex tikseb 17.

$$B=\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(5+2\sqrt{2}\right)}{17}$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' \sqrt{2}-\sqrt{7} b'kull terminu ta' 5+2\sqrt{2}.

$$B=\frac{5\sqrt{2}+2\left(\sqrt{2}\right)^{2}-5\sqrt{7}-2\sqrt{7}\sqrt{2}}{17}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$B=\frac{5\sqrt{2}+2\times 2-5\sqrt{7}-2\sqrt{7}\sqrt{2}}{17}$$

Immultiplika 2 u 2 biex tikseb 4.

$$B=\frac{5\sqrt{2}+4-5\sqrt{7}-2\sqrt{7}\sqrt{2}}{17}$$

Biex timmultiplika \sqrt{7} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$B=\frac{5\sqrt{2}+4-5\sqrt{7}-2\sqrt{14}}{17}$$

Iddividi kull terminu ta' 5\sqrt{2}+4-5\sqrt{7}-2\sqrt{14} b'17 biex tikseb\frac{5}{17}\sqrt{2}+\frac{4}{17}-\frac{5}{17}\sqrt{7}-\frac{2}{17}\sqrt{14}.

$$B=\frac{5}{17}\sqrt{2}+\frac{4}{17}-\frac{5}{17}\sqrt{7}-\frac{2}{17}\sqrt{14}$$

Assenja B (complex solution)

$$B≔\frac{\left(\sqrt{2}-\sqrt{7}\right)\left(2\sqrt{2}+5\right)}{17}$$

Assenja B

$$B≔\frac{5\sqrt{2}+4-2\sqrt{14}-5\sqrt{7}}{17}$$