SOLUTION: Suppose the ages of two siblings are consecutive odd integers. If the product of their ages is 35, what is the age (in years) of the younger sibling? (Enter an exact number.)

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Question 951961: Suppose the ages of two siblings are consecutive odd integers. If the product of their ages is 35, what is the age (in years) of the younger sibling? (Enter an exact number.)
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
y=younger; y+2=older
(y)(y+2)=35
y^2+2y-35=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B2y%2B-35+=+0) has the following solutons:

y%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=%282%29%5E2-4%2A1%2A-35=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+144+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%282%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+5
y%5B2%5D+=+%28-%282%29-sqrt%28+144+%29%29%2F2%5C1+=+-7

Quadratic expression 1y%5E2%2B2y%2B-35 can be factored:
1y%5E2%2B2y%2B-35+=+1%28y-5%29%2A%28y--7%29
Again, the answer is: 5, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-35+%29

ANSWER The age of the younger sibling is 5.
y+2=5+2=7 The older sibling is 7.