Question

If m – n = 16 and m2 + n2 = 400, then find mn.

Answer 1

$m-n = 16$

Squaring both sides,[/tex]

$(m-n)² = (16)²$

$\implies m²+n²-2mn = 256$

$\implies 400-2mn = 256 \;\;\;\; [∵m²+n²=400]$

$\implies 2mn = 400-256$

$\implies 2mn = 144$

$\implies mn = \large \frac{144}{2}$

$\implies mn = 72$