SOLUTION: Good day The square of a natural number is four times more than two times another natural number. The second number is two less than three times the first number. Determine the

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Question 915418: Good day
The square of a natural number is four times more than two times another natural number. The second number is two less than three times the first number. Determine the two natural numbers algebraically
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 = 4(2y)
y = 3x - 2
x^2 = 8(3x-2)]
x^2 = 24x - 16
x^2 - 24x + 16 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-24x%2B16+=+0) has the following solutons:

x%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=%28-24%29%5E2-4%2A1%2A16=512.

Discriminant d=512 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--24%2B-sqrt%28+512+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+512+%29%29%2F2%5C1+=+23.3137084989848
x%5B2%5D+=+%28-%28-24%29-sqrt%28+512+%29%29%2F2%5C1+=+0.686291501015239

Quadratic expression 1x%5E2%2B-24x%2B16 can be factored:
1x%5E2%2B-24x%2B16+=+1%28x-23.3137084989848%29%2A%28x-0.686291501015239%29
Again, the answer is: 23.3137084989848, 0.686291501015239. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-24%2Ax%2B16+%29