SOLUTION: Find two consecutive numbers such that if twice the larger is added to four times the square of the smaller. The sum will be 112.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Find two consecutive numbers such that if twice the larger is added to four times the square of the smaller. The sum will be 112.      Log On


   

Question 83666: Find two consecutive numbers such that if twice the larger is added to four times the square of the smaller. The sum will be 112.
Answer by Mona27(45) About Me  (Show Source):
You can put this solution on YOUR website!
First you give a name to the two consecutive numbers to make things easier:
If you call the first one x, then the next one is x+1.
If twice the larger is added to four times the square of the smaller, the sum will be 112.
2%28x%2B1%29+%2B+4x%5E2+=+112
2x+%2B+2+%2B+4x%5E2+=+112
Subtracting 2 from both sides:
4x%5E2%2B2x+=+110
You can divide through by 2:
2x%5E2%2Bx=55
Now rearrange your equation to look something like this:
2x%5E2%2Bx-55=0
Factorising:
%282x%2B11%29%28x-5%29=0
So this gives either x=-5.5 or x=5
the first number is rejected so we'll take the second.
So your two numbers are: 5 & 6