Question

Find the value of a and b if root 2+1/root 2-1-root2-1/root 2+1=a+root 2b

Answer 1

$\textbf{\underline{\huge{Solution :}}}$

$\textbf{Concept : 1. Taking L.C.M} \\ \\ \textbf{2. Using algebraic identities}$

$\bold{\frac{ \sqrt{2} + 1 }{ \sqrt{2} - 1} - \frac{1}{ \sqrt{2} + 1} = a + \sqrt{2} b} \\ \\ \bold{ \frac{( \sqrt{2} + 1)( \sqrt{2} + 1) - 1( \sqrt{2} - 1)}{( \sqrt{2} - 1)( \sqrt{2} + 1)}} \\ \\ \bold{(x + y)(x + y) = {x}^{2} + {y}^{2} + 2xy} \\ \bold{ (x - y)(x + y) = {x}^{2} - {y}^{2}} \\ \\ \bold{= \frac{ { \sqrt{2} }^{2} + 1 + 2 \sqrt{2} - \sqrt{2} + 1 }{ { \sqrt{2} }^{2} - {1}^{2} }} \\ \\ \bold{= \frac{2 + 2+ \sqrt{2} }{2 - 1} } \\ \\ \bold{ 4 + \sqrt{2} = a + \sqrt{2} b}$

$\textbf{ On comparing we get, }$

$\boxed{\textbf{\large{ a = 4 and b = 1 }}}$

Answer 2

Answer:

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