Question

Difference between the squares of two numbers is 80.The square of the smaller number is 8 times bigger than the bigger number. Find the two numbers

Answer 1

It's 180 not 80.
$let \: \: larger \: \: \: number = x$
(smaller)² = 8x
x²-8x-180=0
x²+10x-18x-180=0
x(x+10) - 18(x+10) =0
(x-18) (x+10) =0
therefore, x=18.
$rejecting \: x = - 10$
Larger number = x = 18
smaller number =
$\sqrt{8 \times 18}$
$\sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3}$
$2 \times 2 \times 3$
$12$