SOLUTION: Suppose that the sum of two numbers is 16, and the sum of their squares is 178. Find the numbers..

Question 628787: Suppose that the sum of two numbers is 16, and the sum of their squares is 178. Find the numbers..
Answer by graphmatics(170) (Show Source): You can put this solution on YOUR website!
x+y=16. So y=16-x
x*x+(16-x)*(16-x)=178 x*x+16*16-32x+x*x=178 2*x*x-32x+256-178=0 2*x*x-32x+78=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=400 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 13, 3. Here's your graph:

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