SOLUTION: one positive number is 4 more than another. The sum of their squares is 40. what are the numbers ?

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Question 246343: one positive number is 4 more than another. The sum of their squares is 40. what are the numbers ?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
let n and m =the numbers
n=4+m
n^2+m^2=40
substitute
(m+4)^2+m^2=40
m^2+8m+16+ m^2=40
2m^2+8m+16-40=0
2m^2+8m-24=0
divide by 2
m^2+4m-12=0
we can only use the positive answer
n=2
m=2+4=6
so we have 2+4=6 for the other number
2^2+6^2=40
4+36=40
40=40
check
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-12+=+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=%284%29%5E2-4%2A1%2A-12=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+2
x%5B2%5D+=+%28-%284%29-sqrt%28+64+%29%29%2F2%5C1+=+-6

Quadratic expression 1x%5E2%2B4x%2B-12 can be factored:
1x%5E2%2B4x%2B-12+=+1%28x-2%29%2A%28x--6%29
Again, the answer is: 2, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-12+%29