Question

The sum of two positive numbers x and y (x> y) is 50 and the difference of their squares is 720. Find the numbers.

Answer 1

Given: $x+y=50-----\left(1\right)x^2-y^2=720(x-y)(x+y)=720(x-y)\times 50=720x-y=\frac{720}{50}x-y=14.4-----\left(2\right)$

By adding equation (1) and (2), we get $2x=64.4$
$\Rightarrow x=32.2$
Substitute $x=32.2$ in equation (1), we get $x=50-32.2=17.8$
Therefore, the numbers are 32.2 and 17.8.