If a, b are rational numbers and (a – 1) √ 2 + 3 =b√2+ a, the value of (a + b) is

The correct option is 5.

Let us solve this step-by-step to find the value of $a+b$ using the given equation:

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

Here, we are given that $a$ and $b$ are rational numbers. Since $\sqrt{2}$ is an irrational number, we can equate the rational parts and the irrational parts from both sides of the equation.

Let us group the terms with $\sqrt{2}$ (irrational parts) and the terms without $\sqrt{2}$ (rational parts):

On the left-hand side (LHS):
Irrational part coefficient = $a-1$
Rational part = $3$

On the right-hand side (RHS):
Irrational part coefficient = $b$
Rational part = $a$

Equating the rational parts from both sides, we get:
$a=3$

Equating the coefficients of $\sqrt{2}$ (irrational parts) from both sides, we get:
$a-1=b$

Substitute the value of $a=3$ into the equation for $b$:
$3-1=b$
$b=2$

Now, we can find the value of $a+b$:
$a+b=3+2=5$

Thus, the value of $a+b$ is indeed 5.