Question : If $a − b = 8$ and $ab = 9$, then the value of $a + b$ is ______.
Option 1: $\pm 9$
Option 2: $\pm 7$
Option 3: $\pm 8$
Option 4: $\pm 10$
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Correct Answer: $\pm 10$
Solution :
Given, $a − b = 8$ and $ab = 9$
Consider, $a-b = 8$
Squaring both sides,
⇒ $a^2 + b^2 - 2ab = 64$
⇒ $a^2 + b^2 - 2\times 9 = 64$
⇒ $a^2 + b^2 = 64+ 18$
⇒ $a^2 + b^2 = 82$
Now we have to find $a+b$
$(a+b)^2 = a^2 + b^2 + 2ab$
$= 87 + 2\times 9$
$=82 + 18$
$= 100$
⇒ $a+b = \sqrt{100}$
⇒ $a+b = \pm 10$
Hence, the correct answer is $\pm 10$.
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