Let first number be x
second number be: x-7
From x - y =7
-y = -x +7
y = x - 7
The square of the sum of two numbers : (x + x - 7)²
Equation:
(x + x - 7)² = 289
4x² - 28x + 49 - 289 = 0
4x² - 28x - 240 = 0
Factor the quadratic equation:
4 (x-12) (x+5) = 0
x-12 = 0 x +5 = 0
x = 12 x = -5
The numbers are:
x = 12 and
x-7 = 12-7 = 5
FINAL ANSWER: 12 and 5
To check:
12-5 = 7
(12 + 5)² = 289
(17)² = 289
289 = 289