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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