SOLUTION: One number is one less than twice another, and the difference between their squares is 16. Find the numbers

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Question 980893: One number is one less than twice another, and the difference between their squares is 16. Find the numbers
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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x=one number; y=other number
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x=2y-1
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x%5E2-y%5E2=16
%282y-1%29%5E2-y%5E2=16
4y%5E2-4y%2B1-y%5E2=16
3y%5E2-4y-15=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 3y%5E2%2B-4y%2B-15+=+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=%28-4%29%5E2-4%2A3%2A-15=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+196+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+196+%29%29%2F2%5C3+=+3
y%5B2%5D+=+%28-%28-4%29-sqrt%28+196+%29%29%2F2%5C3+=+-1.66666666666667

Quadratic expression 3y%5E2%2B-4y%2B-15 can be factored:
3y%5E2%2B-4y%2B-15+=+3%28y-3%29%2A%28y--1.66666666666667%29
Again, the answer is: 3, -1.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-15+%29

y=3 or y=-1.67
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For y=3:
x=2y-1=2(3)-1=6-1=5
ANSWER 1: The numbers are 5 and 3
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For y=-1.67:
x=2y-1=2(-1.67)-1=-4.34
ANSWER 2: The numbers are -1.67 and -4.34