Question 1179118
A number exceed another by 5, the sum of their square is 157. What are the numbers?
Solution:
Let the first number be x. 
Then the second number will be x + 5.
Sum of the squares of the numbers = 157
x^2 + (x + 5)^2 = 157
x^2 + x^2 + 10x + 25 = 157
2x^2 + 10x + 25 - 157 = 0
2x^2 + 10x - 132 = 0
2(x^2 + 5x - 66) = 0
x^2 + 5x - 66 = 0/2
x^2 + 11x - 6x- 66 = 0
x(x + 11) - 6(x + 11) = 0
(x + 11)(x - 6) = 0
x + 11 = 0     or x - 6 = 0
x = -11   or x = 6
When we take x = -11, x + 5 becomes -11 + 5 = -6
When we take x = 6, x + 5 becomes 6 + 5 = 11
Thus, the two numbers are -11, -6   or 6, 11.