The square of the sum of two numbers is 144 and the sum of their square is 180, find the numbers
Let the two numbers be x and y.
The square of x+y is x^2+2xy+y^2 and that is 144
The sum of x^2 and y^2 is 180.
So you can get from substituting the second equation to the first and you get
So 2xy= -36
xy= - 18
And x+y = 12 or -12
because 12^2 or -12^2 is 144.
(x-y)^2 is x^2-2xy+y^2 which is 180 +36 or 216
So x-y equals 6sqrt6, or -6sqrt6.
Adding and dividing be 2
gives x = 6 + 3sqrt6 and y= 6 - 3sqrt6
And your done