Question

√2-1÷√2+1=a+b√2, then find the values of a and b

Answer 1

Firstly , rationalize the denominator of the LHS....

√2 - 1 / √2 + 1

= (√2 - 1 / √2 + 1) × ( √2 - 1 / √2 - 1)

= ( √2 - 1 )^2 / (√2)^2 - (1)^2

= [ (√2)^2 + (1)^2 - 2×√2×1 ] / 2 - 1

= (2 + 1 - 2√2) / 1

= 3 - 2√2

We know that,

=> 3 - 2√2 = a + b√2

So,

a = 3

a = 3b = - 2