Answer:
The numbers are 6 and 2
Explanation:
Given this scenario, we can set up the following equations:
x + y = 8
x² + y² = 40.
___________
x + y = 8
y = 8 – x
(y)² = (8 – x)²
y² = (8 – x)²
x² + y² = 40
x² + (8 – x)² = 40
x² + 64 – 16x + x² = 40
2x² – 16x + 64 = 40
2x² – 16x = -24
2(x² – 8x) = -24
x² – 8x = -12
x² – 8x + 12 = 0
(x – 6)(x – 2) = 0
x = 6 or 2.
x + y = 8 →
(6 or 2) + y = 8
y = 8 – (6 or 2)
y = 2 or 6.
___________
x + y = 8 →
6 + 2 = 8 →
8 = 8 ✓
x² + y² = 40 →
6² + 2² →
36 + 4 = 40 →
40 = 40 ✓