SOLUTION: find two positive numbers whose squares have a sum of 25 and a difference of 7

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Question 1010246: find two positive numbers whose squares have a sum of 25 and a difference of 7
Answer by farohw(175) About Me  (Show Source):
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Set up your equations then add:
x²+y² = 25
x²-y² = 7
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2x² = 32

Solve 2x² = 32 by dividing both sides by 2:
2x²/2 = 32/2
x² = 16
x = 4

Substitute x = 4 into the first equation to obtain the y value:
x²+y² = 25
(4)²+y² = 25
16+y² = 25
y² = 25 - 16
y² = 9
y = 3

Since x = 4 and y = 3, the two positive numbers are 4 and 3.

Verify:
4²+3² = 25 => 16+9 = 25
4²-3² = 7 => 16 - 9 = 7