SOLUTION: the difference between the square of a number is 35. four times the square of the first number increased by the square of the second number is 145. find the numbers

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Question 830962: the difference between the square of a number is 35. four times the square of the first number increased by the square of the second number is 145. find the numbers
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Something is missing. Maybe you mean, "the difference between the squareS of TWO NUMBERS is 35. Four times the square of the first number increased by the square of the second number is 145. Find the numbers."

numbers, m and n.

m%5E2-n%5E2=35 and 4m%5E2%2Bn%5E2=145, but your wording on that is somewhat ambiguous.

First description gives n%5E2=m%5E2-35
and
Second description gives n%5E2=145-4m%5E2.

Equate the two formulas for n%5E2.
m%5E2-35=145-4m%5E2
m%5E2%2B4m%5E2=145%2B35
5m%5E2=180
m%5E2=36
highlight%28m=6%29 or m=-6
-
If assuming positive numbers, then n%5E2=36-35=1, highlight%28n=1%29.