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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 No Rating

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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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