Question : If $a$ and $b$ are rational numbers and $(a-1)\sqrt2+3=b\sqrt2+a$; then the value of $(a+b)$ is:
Option 1: $–5$
Option 2: $3$
Option 3: $–3$
Option 4: $5$
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Correct Answer: $5$
Solution :
Given: $(a-1)\sqrt2+3=b\sqrt2+a$
In comparison, we get the values of $a=3$ and $(a-1)=b$, respectively.
Substitute the value of $a=3$ in equation $(a-1)=b$, we get,
$(3-1)=b$
⇒ $b=2$
So, the value of $(a+b)$ is $(3+2)=5$
Hence, the correct answer is 5.
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