Question

the product of the two numbers is 600 and their difference is 4. what are the number

Answer 1

let the numbers are x and y (x>y)
so xy=600 and x-y=4
so
${(x + y)}^{2} = {(x - y)}^{2} + 4xy \\ = {4}^{2} + 4 \times 600 \\ = 24 + 2400 \\ = 2424$
so here you can find x+y
$x + y = \sqrt{2424}$
so x+y+x-y=2x=
$2x = \sqrt{2424} + 4$
so you can find x and put the value of x in
x-y=4
and there you can find y