Question

answer the question ​

Answer 1

Answer:

$\textbf{Given:–} \: \frac{ \sqrt{7} - 2}{ \sqrt{7} + 2 } = a \sqrt{7} + b$

$\textbf{Find:– } \text{the value of a and b }$

Solution:

$\text{On Solving L.H.S}$

$= \frac{ \sqrt{7} - 2}{ \sqrt{7} + 2}$

$\text{on Rationalisation}$

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

$= \frac{( \sqrt{7} - 2 {)}^{2} }{( \sqrt{7} {)}^{2} - (2 {)}^{2} }$

$= \frac{( \sqrt{7} {)}^{2} + (2 {)}^{2} - 2(2) \sqrt{7} }{7 - 4}$

$= \frac{7 + 4 - 4 \sqrt{7} }{3}$

$= \frac{4 \sqrt{7} + 11}{3}$

$= \frac{ - 4 \sqrt{7} }{3} + \frac{11}{3}$

$\textbf{On Comparing L.H.S and R.H.S}$

$\textbf{Hence,} \frac{ - 4 \sqrt{7} }{3} + \frac{11}{3} = a \sqrt{7} + b$

$\textbf{Here} \: a = \frac{ - 4}{3} \: \text{and} \: b = \frac{11}{3}$

$\\ \\ \\ \\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$