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

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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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-32x%2B78+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-32%29%5E2-4%2A2%2A78=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--32%2B-sqrt%28+400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-32%29%2Bsqrt%28+400+%29%29%2F2%5C2+=+13
x%5B2%5D+=+%28-%28-32%29-sqrt%28+400+%29%29%2F2%5C2+=+3

Quadratic expression 2x%5E2%2B-32x%2B78 can be factored:
2x%5E2%2B-32x%2B78+=+2%28x-13%29%2A%28x-3%29
Again, the answer is: 13, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-32%2Ax%2B78+%29