SOLUTION: Find two numbers whose product is 156 if the sum of their squares is 313. Show your work.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find two numbers whose product is 156 if the sum of their squares is 313. Show your work.      Log On


   

Question 958059: Find two numbers whose product is 156 if the sum of their squares is 313. Show your work.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A%2AB=156
A%5E2%2BB%5E2=313
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%28A%2BB%29%5E2=A%5E2%2B2AB%2BB%5E2=313%2B2%28156%29=625
1.A%2BB=25
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%28A-B%29%5E2=A%5E2-2AB%2BB%5E2=313-2%28156%29=1
2.A-B=1
Adding eq. 1 and 2,
A%2BB%2BA-B=25%2B1
2A=26
A=13
and
13%2BB=25
B=12
The two numbers are 12 and 13.
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We could have also taken the negative square root.
3.A%2BB=-25
4.A-B=-1
2A=-26
A=-13
-13%2AB=156
B=-12
The two numbers are also -12 and -13.