Question

√2-1/√2+1=a+b√2 find a and b​

Answer 1

Answer -

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Answer 2

$\huge \boxed{ \bf{Answer}}$


$\bf \underline{ To \: find \: a \: and \: b \: where:} \: \: \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1 } = a + b \sqrt{2}$


Solving L.H.S,

$= \frac{ \sqrt{2} - 1}{ \sqrt{2} + 1 }$

Multiplying both numerator and denominator by (√2 -1)

$= \frac{( \sqrt{2} - 1)( \sqrt{2} - 1) }{ (\sqrt{2} + 1)( \sqrt{2} - 1) }$

$= \frac{ ({ \sqrt{2} - 1) }^{2} }{ ({ \sqrt{2}) }^{2} - {1}^{2} }$

$= \: \frac{ ({ \sqrt{2} )}^{2} + 1 - 2 \sqrt{2} }{2 - 1}$

$= 2 + 1 - 2 \sqrt{2}$

$= 3 - 2 \sqrt{2}$


Now, on comparing with R.H.S we get

$= > \: 3 - 2 \sqrt{2} = \: a \: + b \sqrt{2}$


$\boxed {\underline{ \bf{a \: = 3 \: \: and \: \: b = - 2 }}}$