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Sum of powers (Posted on 2015-11-18)

Given a+b=1 & a^2+b^2 =25,

Find a^4+b^4, without solving for a and b.

No Solution Yet Submitted by Ady TZIDON

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Solution

| Comment 1 of 3

Square the first equation

a^2+2ab+b^2=1

2ab+25=1

ab=-12

(ab)^2=144

Square the second equation

a^4+2(ab)^2+b^4=625

a^4+b^4=625-2(ab)^2

a^4+b^4=625-2(144)=337.

p.s.

Squaring -12 bothered me, so to confirm the solution I did solve for a and b with a graph: (4,-3) or (-3,4). And indeed 3^4+4^4=337.

Posted by Jer on 2015-11-18 08:33:17

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