SOLUTION: The difference of two positive numbers is 6 and the sum of their squares is 90. Find the numbers.

Question 222042: The difference of two positive numbers is 6 and the sum of their squares is 90. Find the numbers.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the larger of the two positive numbers. Let

represent the smaller of the two positive numbers.

The difference is 6, so:

The larger number squared is:

and the smaller number squared is:

And the sum of the two squares is then:

In standard form:

Divide by 2:

Solve for

to get the larger number. Subtract 6 to get the smaller. Hint: The quadratic factors. You will get two roots. Exclude the negative root because the problem says you are looking for a positive integer.

John

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