Question

the sum of two numbers is 8. the sum of the squares of the same two numbers is 40. what are the numbers?​

Answer 1

Answer:

The numbers are 6 and 2

Step-by-step 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 ✓