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