Question

Find rational number a and b such that √2-1\√2+1=a+b root 2

Answer 1

see this it will help u

Answer 2

Answer:

The value are a=3 and b=-2

Step-by-step explanation:

Given expression

$\frac{\sqrt2-1}{\sqrt2+1}=a+b\sqrt2$

we have to find the rational number a and b

$\frac{\sqrt2-1}{\sqrt2+1}=a+b\sqrt2$

Rationalizing left side

$\frac{\sqrt2-1}{\sqrt2+1}\times \frac{\sqrt2-1}{\sqrt2-1}=a+b\sqrt2$

$\frac{(\sqrt2-1)^2}{(\sqrt2+1)(\sqrt2-1)}=a+b\sqrt2$

$\frac{2+1-2\sqrt2}{2-1}=a+b\sqrt2$

$3-2\sqrt2=a+b\sqrt2$

Comparing above we get

a=3 and b=-2