Question 542384: Two numbers differ by 7,the different of their squares is 91,find the numbers.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two numbers differ by 7,the different of their squares is 91,find the numbers.
Two numbers: a, b
a - b = 7
a = (b+7)
:
a^2 - b^2 = 91
:
Replace a with (b+7)
(b+7)^2 - b^2 = 91
:
FOIL (b+7)(b+7)
b^2 + 14b + 49 - b^2 = 91
b^2 - b^2 + 14b = 91 - 49
14b = 42
b = 42/14
b = 3
:
Find a
a = 3 + 7
a = 10
:
:
Check: 10^2 - 3^2 = 91
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