SOLUTION: The product of two numbers is 72. The difference is 14.what is the sum of the two numbers ? .thanks for any help.

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Question 1075303: The product of two numbers is 72. The difference is 14.what is the sum of the two numbers ? .thanks for any help.
Found 2 solutions by josgarithmetic, Aaragorn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
system%28xy=72%2Cy-x=14%29

You could try checking factorizations of 72.
72=2%2A36=3%2A24=highlight_green%284%2A18%29=6%2A12=9%2A8, and the green-outlined combination is the one that will work.

Answer by Aaragorn(2) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 2 no.s be x and y and,
Let x be greater than y, that is x > y
From the question,
The product of the two no.s is 72
That is xy = 72 => 4xy = 288
and,
The difference between the two no.s is 14
That is x - y = 14

We know that,
(x + y)^2 = x^2 + y^2 + 2xy
= x^2 + y^2 - 2xy + 4xy
= (x - y)^2 + 4xy
= (14)^2 + (288)
= 196 + 288
= 484
=> x + y = sqrt(484) = +22 OR - 22
Since we had assumed the two numbers to be x and y
Therefore the sum of x and y is
x + y = +22 OR -22