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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