Question

√2-1/√2+1 = a+b√2,then find the values of a and b are:-​

Answer 1

Answer:

The answer is $a=3,b=-2$

Step-by-step explanation:

$\text{LHS}=\dfrac{\sqrt 2-1}{\sqrt 2+1}$

Rationalize denominator

       $=\dfrac{\sqrt2-1}{\sqrt 2+1}\times \dfrac{\sqrt 2-1}{\sqrt 2-1}\\\\=\dfrac{(\sqrt 2)^2-2(\sqrt 2)+1^2}{(\sqrt2)^2-1^2}$

Using $(a+b)(a-b)=a^2-b^2$ and $(a-b)^2=a^2-2ab+b^2$

     $=\dfrac{2-2\sqrt 2+1}{2-1}=\dfrac{3-2\sqrt2}{1}=3-2\sqrt 2$

     $=a+b\sqrt 2$, given

Therefore $a=3,b=-2$