Question

if a, b are rational numbers and (a-1)√2+3=b√2+a, the value of (a+b) is?

Answer 1

$(a-1)\sqrt{2}+3~=~b\sqrt{2}+a$

Since $a,b$ are rational and $\sqrt{2}$ is irrational, we can compare rational and irrational terms both sides. Comparing terms attached to $\sqrt{2}$ both sides we get :
$a-1=b$

comparing rational terms both sides gives
$3=a$

Plug this in the earlier equation and get
$3-1=b\implies\,b=2$