SOLUTION: The difference of 2 numbers is 180. Square of smaller number is 8 times the larger number. find the numbers?

Question 536342: The difference of 2 numbers is 180. Square of smaller number is 8 times the larger number. find the numbers?
Found 2 solutions by april4869, MathTherapy:
Answer by april4869(19) (Show Source): You can put this solution on YOUR website!
Lets suppose the two numbers are X and Y, where Y is the smaller number of the two, then
x^2 - y^2 = 180-----------1
the square of the smaller number is eight times the larger number, so
y^2 = 8x--------------------2
So, using equation 2 in equation 1, we have
x^2 - 8x = 180
x^2 - 8x - 180 = 0
splitting -8x into 10x - 18x
x^2 +10x - 18x - 180 = 0
x(x+10) -18(x+10) = 0
(x - 18)(x +10) = 0
so x = 18 or x = -10
If x = 18, using equation 2,
y^2 = 8 X 18 = 144
then y = +-12
If x = -10, using equation 2,
y^2 = 8 X -10 = -80
then y will be an imaginary number.
considering you are using only real numbers, the solution will be x = 18 and y = +-12.
Answer by MathTherapy(10553) (Show Source): You can put this solution on YOUR website!
The difference of 2 numbers is 180. Square of smaller number is 8 times the larger number. find the numbers?

Let the larger and smaller numbers be L and S, respectively
Then: L � S = 180 ------ L = 180 + S ------ eq (i)
----- ------- eq (ii)

------ Substituting 180 + S for L in eq (ii)

Solving using the quadratic formula, we find that S, or smaller number = , or

If smaller number = , then larger number =

However, if smaller number = , then larger number =

I'm sure you can do the check!!

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