Question

The sum of two numbers is 11. The sum of their squares is 65. Find the numbers. (How do you get the answer?)

Answer 1

X is the number
The sum of two numbers is 11, so other number is : 11 - x

The sum of their squares is 65

x^2 + (11 - x)^2 = 65
x^2 + 121 - 2(x)(11) + x^2 = 65
2x^2 - 22x + 121 = 65
2x^2 - 22x + 121 -  65 = 0
2x^2 - 22x + 56 = 0
2(x^2 - 11x + 28) = 0
2(x - 7)(x -4 ) = 0
x - 7 = 0
x = 7

x - 4 =0
x =4

answer: the numbers are 4 and 7

double check:

sum of two numbers is 11:
4 + 7 = 11

The sum of their squares is 65
4^2 + 17^2 = 16 + 49 = 65