Question

If a, b are rational numbers and $\left(a-1\right)\sqrt{2}+3=b\sqrt{2}+a$, 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,

$\Rightarrow$ $a-1=b$ ---- ( 1 )

Comparing rational terms both sides gives

$\Rightarrow$ $3=a$ ---- ( 2 )

Substituting ( 2 ) in ( 1 ),

$\Rightarrow$ $3-1=b$

$\therefore$ $b=2$

$\Rightarrow$ $a+b=3+2=5$