The sum of the squares of two negative numbers is 89 and the difference of the squares of the numbers is 39. Find the numbers

Answer 1

Let's assume the two negative numbers are x and y.

Given:
x^2 + y^2 = 89
x^2 - y^2 = 39

Add the two equations together:
2x^2 = 128
x^2 = 64
x = -8

Substitute x back into the first equation:
64 + y^2 = 89
y^2 = 25
y = -5

Therefore, the two numbers are -8 and -5.