SOLUTION: I have an algebra project and one of the questions says " The difference between two perfect squares is 133.What is the smallest possible sum of the two perfect squares? " I found
Question 735490: I have an algebra project and one of the questions says " The difference between two perfect squares is 133.What is the smallest possible sum of the two perfect squares? " I found out that the answer is 205, but I don't understand why that is the answer. Found 2 solutions by stanbon, Edwin McCravy:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! I have an algebra project and one of the questions says " The difference between two perfect squares is 133.What is the smallest possible sum of the two perfect squares? " I found out that the answer is 205, but I don't understand why that is the answer.
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Equation:
x^2 - y^2 = 133
(x-y)(x+y) = 133
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133 = 7*19 = (13-6)(13+6)
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Ans: 13^2+6^2 = 169 + 36 = 205
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Cheers,
Stan H.
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x² - y² = 133
(x - y)(x + y) = 133
So (x - y) and (x + y) are factors of 133
and (x - y) is the smaller factor and (x + y)
is the larger factor.
The only two ways to factor 133 are
1·133 where 1 is the smaller and 133 is the larger.
and
7·19 where 7 is the smaller and 19 is the larger.
In the first case we have
x - y = 1
x + y = 133
Solve that system and get solution x=67, y=66
The sum of their squares is 67²+66² = 4489 + 4356 = 8845
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In the second case we have
x - y = 7
x + y = 19
Solve that system and get solution x=13, y=6
The sum of their squares is 13²+6² = 169 + 36 = 205
Edwin
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