Question 983431
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^3 + 343 - 147x^2 + 147x - x^3 = 133}}}
{{{147x^2 - 147x - 210 = 0}}}
{{{7x^2 - 7x - 10 = 0}}}
It's easy to solve for x when you know the answer.