SOLUTION: One integer is 8 less than 5 times another. Their product is 21. Find the integers.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: One integer is 8 less than 5 times another. Their product is 21. Find the integers.      Log On


   

Question 950499: One integer is 8 less than 5 times another. Their product is 21. Find the integers.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
a and b are integers
a*b=21
a=21/b
a=5b-8 Substitute for a
21/b=5b-8 Multiply each side by b
21=5b^2-8b Subtract 21 from each side.
0=5b^2-8b-21
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ab%5E2%2Bbb%2Bc=0 (in our case 5b%5E2%2B-8b%2B-21+=+0) has the following solutons:

b%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=%28-8%29%5E2-4%2A5%2A-21=484.

Discriminant d=484 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+484+%29%29%2F2%5Ca.

b%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+484+%29%29%2F2%5C5+=+3
b%5B2%5D+=+%28-%28-8%29-sqrt%28+484+%29%29%2F2%5C5+=+-1.4

Quadratic expression 5b%5E2%2B-8b%2B-21 can be factored:
5b%5E2%2B-8b%2B-21+=+5%28b-3%29%2A%28b--1.4%29
Again, the answer is: 3, -1.4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-8%2Ax%2B-21+%29

The integer answer is 3 so ANSWER: One of the numbers is 3.
a=21/b=21/3=7 ANSWER 2: The other integer is 7.
CHECK:
a=5(b)-8
7=5(3)-8
7=15-8
7=7