SOLUTION: Find three consecutive positive integers such that twice the product of the two smaller integers is 88 more than the product of the two larger integers.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Find three consecutive positive integers such that twice the product of the two smaller integers is 88 more than the product of the two larger integers.       Log On


   

Question 316961: Find three consecutive positive integers such that twice the product of the two smaller integers is 88 more than the product of the two larger integers.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x,x+2,x+4
x and x+2 are the 2 smaller numbers
2%28x%28x%2B2%29%29=88%2B%28%28x%2B2%29%28x%2B4%29%29 "twice the product of the two smaller integers is 88 more than the product of the two larger integers"
%282x%5E2%2B4x%29=88%2B%28x%5E2%2B6x%2B8%29 add
2x%5E2%2B4x=x%5E2%2B6x%2B96 subtract
x%5E2-2x-96=0
doesnt come out to a whole number so either thats suppose to be that way in the answer or the question was written wrong.
x= 10.8488578017961 or -8.8488578017961
(x+2)= 12.8488578017961 or -6.8488578017961
(x+4)= 14.8488578017961 or -4.8488578017961
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-96+=+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=%28-2%29%5E2-4%2A1%2A-96=388.

Discriminant d=388 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+388+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+388+%29%29%2F2%5C1+=+10.8488578017961
x%5B2%5D+=+%28-%28-2%29-sqrt%28+388+%29%29%2F2%5C1+=+-8.8488578017961

Quadratic expression 1x%5E2%2B-2x%2B-96 can be factored:
1x%5E2%2B-2x%2B-96+=+1%28x-10.8488578017961%29%2A%28x--8.8488578017961%29
Again, the answer is: 10.8488578017961, -8.8488578017961. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-96+%29