Question

If √x ­- √y = 1 , √x + √y = 17 then √xy = ?

A) √72 B) 72 C) 32 D) 24

Answer 1

Answer:

$\sqrt{x} - \sqrt{y} = 1 \\ {( \sqrt{x} - \sqrt{y} ) }^{2} = 1 \\ x + y - 2 \sqrt{x} \sqrt{y} = 1 - - - - 1 \\ \\ \sqrt{x} + \sqrt{y} = 17 \\ {( \sqrt{x} + \sqrt{y}) }^{2} = 289 \\ x + y + 2 \sqrt{x} \sqrt{y} = 289 - - - - 2 \\ \\ subtracting \: eq \: 1 \: and \: 2 \\ 4 \sqrt{x} \sqrt{y} = 288 \\ \sqrt{x} \sqrt{y} = 72$

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