Question

Solve this
Q. Values of a $\downarrow$
$\frac{5-\sqrt{6}}{5+\sqrt{6}}=a-b\sqrt{6}$

Answer 1

Dear Student,

$$\begin{gathered} \frac{5-\sqrt{6}}{5+\sqrt{6}}=a-b\sqrt{6} \\ OnrationalizingL.H.S \\ weget, \\ \frac{{\displaystyle 5-\sqrt{6}}}{{\displaystyle 5+\sqrt{6}}}\times \frac{{\displaystyle 5-\sqrt{6}}}{{\displaystyle 5-\sqrt{6}}} \\ =\frac{{\displaystyle {\left(5-\sqrt{6}\right)}^2}}{{\displaystyle 5^2-{\sqrt{6}}^2}} \\ =\frac{25+6-10\sqrt{6}}{25-6}\left[{\left(a-b\right)}^2=a^2+b^2-2ab\right] \\ =\frac{31-10\sqrt{6}}{19} \\ itcanalsowrittenas \\ =\frac{31}{19}-\frac{10}{19}\sqrt{6} \\ Hence \\ \mathit{a}\mathbf{=}\frac{\mathbf{31}}{\mathbf{19}}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathbf{}\mathit{b}\mathbf{=}\frac{\mathbf{10}}{\mathbf{19}} \end{gathered}$$

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