Question

√2-1/√2+1=a-b√2 rationalise the denominator​

Answer 1

√3-1\√3+1=a-b√3

(Rationalize the denominator)

In LHS(left hand side)

= (√3-1)(√3-1)\(√3+1)(√3-1)

= 3+1-2√3\3-1

=4-2√3\2

(Taking 2 common from numerator)

=2-√3 (1)

In RHS

a-b√3. (2)

A.T.Q(according to question)

(1)=(2)

2-√3=a-b√3 (Comparing both equations)

So, a=2,b=1.

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Answer 2

$LHS = \frac{(\sqrt{2}-1)}{(\sqrt{2}+1)} \\= \frac{(\sqrt{2}-1)(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)} \\= \frac{(\sqrt{2}-1)^{2}}{(\sqrt{2})^{2} - 1^{2} }\\= \frac{(\sqrt{2})^{2} - 2\times \sqrt{2}\times 1 + 1^{2} }{2-1}\\= 2-2\sqrt{2}+1\\= 3-2\sqrt{2} \: --(1)$

$Compare \:this \:with \: RHS = a - b\sqrt{2} ,we\:get$

$a = 3 , b = 2$

Therefore.,

$a = 3 , b = 2$

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