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: $5$

Question

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: $5$

Team Careers360 · Accepted Answer

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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Question : If a and b are rational numbers and (a−1)2+3=b2+a; then the value of (a+b) is:Option 1: –5Option 2: 3Option 3: –3Option 4: 5

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Question : If $a$ and $b$ are rational numbers and $(a - 1) \sqrt{2} + 3 = b \sqrt{2} + a$ ; then the value of $(a + b)$ is:
Option 1: $- 5$
Option 2: $3$
Option 3: $- 3$
Option 4: $5$