SOLUTION: A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 31. Find the numbers.

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Question 1045080: A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 31. Find the numbers.

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 31. Find the numbers.
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Let x be the smallest of the two numbers.
Then the other number is x+2.


And your equation is 

x%5E2+%2B+4%2A%28x%2B2%29 = 31.

Simplify and solve it:

x%5E2+%2B+4x+-+23 = 0.

It is not "factorable" with integer coefficients.

Apply the quadratic formula.


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 31. Find the numbers.
Let larger number be L
Then smaller = L - 2
We then get: 4L+%2B+%28L+-+2%29%5E2+=+31
4L+%2B+L%5E2+-+4L+%2B+4+=+31
L%5E2+=+27
L, or larger number = highlight_green%28matrix%281%2C3%2C+sqrt%2827%29%2C+or%2C+3sqrt%283%29%29%29
Smaller number: highlight_green%283sqrt%283%29+-+2%29