Question : If $\sqrt x-\sqrt y=1$ , $\sqrt x+\sqrt y=17$, then $\sqrt {xy}=?$
Option 1: $\sqrt{72}$
Option 2: $72$
Option 3: $32$
Option 4: $24$
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Correct Answer: $72$
Solution :
$\sqrt{x}-\sqrt{y} = 1$------(1)
⇒ $\sqrt{x} =1 +\sqrt{y}$
Inserting the value of $\sqrt{x}$ in the other equation, we get,
$\sqrt{x} +\sqrt{y} = 17$
⇒ $1+\sqrt{y} +\sqrt{y} = 17$
⇒ $2\sqrt{y} = 16$
⇒ $\sqrt{y} = 8$
Putting the value of $\sqrt{y} = 8$ in equation (1), we get,
$\sqrt{x} - 8= 1$
$\therefore \sqrt{x} = 9$
So, $\sqrt{xy} = \sqrt{x} × \sqrt{y} = 9 × 8 = 72$
Hence, the correct answer is $72$.
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