SOLUTION: IF THE SUM OF TWO NUMBERS IS 7 AND THE SUM OF THEIR CUBES IS 133 FIND THE SUM OF THEIR SQUARES?

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Question 983431: IF THE SUM OF TWO NUMBERS IS 7 AND THE SUM OF THEIR CUBES IS 133 FIND THE SUM OF THEIR SQUARES?
Answer by Alan3354(69443) About Me  (Show Source):
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IF THE SUM OF TWO NUMBERS IS 7 AND THE SUM OF THEIR CUBES IS 133 FIND THE SUM OF THEIR SQUARES?
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They're small numbers, to trial and error is the easiest way.
1 & 6 --> 1 + 216 = 217 NG
2 & 5 --> 8 + 125 = 133
You can find the squares of 2 & 5.
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If the numbers were larger, or not integers:
x + y = 7
x^3 + y^3 = 133
Sub for y, y = 7-x
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x^3 + (7-x)^3 = 133
x%5E3+%2B+343+-+147x%5E2+%2B+147x+-+x%5E3+=+133
147x%5E2+-+147x+-+210+=+0
7x%5E2+-+7x+-+10+=+0
It's easy to solve for x when you know the answer.