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

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

Lahendage ja leidke B

$$B=\frac{5\sqrt{2}+4-2\sqrt{14}-5\sqrt{7}}{17}\approx -0,567117854$$

Juhised lineaarvõrrandi lahendamiseks

Tegurda 8=2^{2}\times 2. Kirjutage \sqrt{2^{2}\times 2} toote juured, kui see ruut \sqrt{2^{2}}\sqrt{2}. Leidke 2^{2} ruutjuur.

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

Ratsionaliseerige korrutades lugeja ja 5+2\sqrt{2} nimetaja \frac{\sqrt{2}-\sqrt{7}}{5-2\sqrt{2}} nimetaja.

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

Mõelge valemile \left(5-2\sqrt{2}\right)\left(5+2\sqrt{2}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Arvutage 2 aste 5 ja leidke 25.

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

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

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

Arvutage 2 aste -2 ja leidke 4.

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

\sqrt{2} ruut on 2.

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

Korrutage 4 ja 2, et leida 8.

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

Lahutage 8 väärtusest 25, et leida 17.

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

Rakendage distributiivsusomadus, korrutades avaldise \sqrt{2}-\sqrt{7} iga liikme avaldise 5+2\sqrt{2} iga liikmega.

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

\sqrt{2} ruut on 2.

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

Korrutage 2 ja 2, et leida 4.

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

\sqrt{7} ja \sqrt{2} korrutage numbrid, mis on sama juur.

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

Jagage 5\sqrt{2}+4-5\sqrt{7}-2\sqrt{14} iga liige 17-ga, et saada \frac{5}{17}\sqrt{2}+\frac{4}{17}-\frac{5}{17}\sqrt{7}-\frac{2}{17}\sqrt{14}.

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

Määra B (complex solution)

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

Määra B

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