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

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

Atrast B

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

Lineāra vienādojuma risināšanas darbības

Sadaliet reizinātājos 8=2^{2}\times 2. Pārrakstiet reizinājuma kvadrātsakni \sqrt{2^{2}\times 2} kā kvadrātveida saknes \sqrt{2^{2}}\sqrt{2}. Izvelciet kvadrātsakni no 2^{2}.

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

Atbrīvojieties no iracionalitātes saucēju ar \frac{\sqrt{2}-\sqrt{7}}{5-2\sqrt{2}}, reizinot skaitītāju un saucēju ar 5+2\sqrt{2}.

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

Apsveriet \left(5-2\sqrt{2}\right)\left(5+2\sqrt{2}\right). Reizināšanu var pārvērst par kvadrātu starpību, izmantojot šo kārtulu: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Aprēķiniet 5 pakāpē 2 un iegūstiet 25.

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

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

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

Aprēķiniet -2 pakāpē 2 un iegūstiet 4.

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

Skaitļa \sqrt{2} kvadrāts ir 2.

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

Reiziniet 4 un 2, lai iegūtu 8.

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

Atņemiet 8 no 25, lai iegūtu 17.

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

Izmantojiet distributīvo īpašību, katru \sqrt{2}-\sqrt{7} locekli reizinot ar katru 5+2\sqrt{2} locekli.

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

Skaitļa \sqrt{2} kvadrāts ir 2.

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

Reiziniet 2 un 2, lai iegūtu 4.

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

Lai reiziniet \sqrt{7} un \sqrt{2}, reiziniet numurus zem kvadrātveida saknes.

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

Daliet katru 5\sqrt{2}+4-5\sqrt{7}-2\sqrt{14} locekli ar 17, lai iegūtu \frac{5}{17}\sqrt{2}+\frac{4}{17}-\frac{5}{17}\sqrt{7}-\frac{2}{17}\sqrt{14}.

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

Piešķiriet B (complex solution)

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

Piešķiriet B

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