SOLUTION: The difference of square of 2 number is 180. The square of smaller number is 8 times the larger number. Find the two numbers.

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Question 534075: The difference of square of 2 number is 180. The square of smaller number is 8 times the larger number. Find the two numbers.
Answer by boilpoil(127) About Me  (Show Source):
You can put this solution on YOUR website!
Let the smaller number be x
Then the larger number be x%5E2%2F8

%28x%5E2%2F8%29%5E2-x%5E2=180
%28x%5E%282%282%29%29%2F8%5E2%29-x%5E2=180
x%5E4%2F64-x%5E2=180
64%28x%5E4%2F64%29-64%28x%5E2%29=64%28180%29
x%5E4-64x%5E2=11520
x%5E4-64x%5E2-11520=0
%28x%5E2%2B80%29%28x%5E2-144%29=0
%28x%5E2%2B80%29%28x-12%29%28x%2B12%29=0
1. x^2+80=0
2. x-12=0 ***Set each of the factors of the equation equal to 0***
3. x+12=0

1. x%5E2=+-80
sqrt%28x%5E2%29=+_sqrt%28-80%29
x=%2B-4i%7B%7B%7Bsqrt%285%29
x=4isqrt%285%29, -4isqrt%285%29

2. x-12=0
x=12

3. x+12=0
x=-12

So x=4isqrt%285%29, -4isqrt%285%29, 12, -12

For the larger number... you calculate yourself just substitute it (I think you are capable of this because you have already started calculating something so complicated as this.

Note: +_ stands for Positive/Negative sign