SOLUTION: One positive number is 3 more than another. The sum of their squares is 149 Find both numbers. We have tried x=1st number and x +3 = 2nd number I have figured that x=7 but I c

Algebra ->  Expressions-with-variables -> SOLUTION: One positive number is 3 more than another. The sum of their squares is 149 Find both numbers. We have tried x=1st number and x +3 = 2nd number I have figured that x=7 but I c      Log On


   

Question 27637: One positive number is 3 more than another.
The sum of their squares is 149 Find both numbers.
We have tried x=1st number
and x +3 = 2nd number
I have figured that x=7 but I cannot get formula written
Thanks
Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
First Number = X
Second Number = X+3
Som of Squares => X%5E2+%2B+%28X%2B3%29%5E2
X%5E2+%2B+X%5E2+%2B+9+%2B6X
2X%5E2+%2B+9+%2B6X
Given that this equals 149
2X%5E2+%2B+9+%2B6X+=+149
Subtracting 149 on both sides
2X%5E2+%2B+9+%2B6X+-+149+=+0
2X%5E2+%2B6X+-+140=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B6x%2B-140+=+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=%286%29%5E2-4%2A2%2A-140=1156.

Discriminant d=1156 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+1156+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+1156+%29%29%2F2%5C2+=+7
x%5B2%5D+=+%28-%286%29-sqrt%28+1156+%29%29%2F2%5C2+=+-10

Quadratic expression 2x%5E2%2B6x%2B-140 can be factored:
2x%5E2%2B6x%2B-140+=+2%28x-7%29%2A%28x--10%29
Again, the answer is: 7, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B6%2Ax%2B-140+%29


Since we are looking for Positive numbers X = 7
which means the second number is 10 :-)