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Sum of powers (Posted on 2015-11-18) Difficulty: 2 of 5
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 A little more direct.... Comment 3 of 3 |
Start with the identity:
a^4+b^4 = (a+b)^2*(a^2+b^2) + [(a^2+b^2)^2 - (a+b)^4]/2

Then substitute:
a^4+b^4 = 1^2*25 + [25^2 - 1^4]/2 = 337

  Posted by Brian Smith on 2016-07-13 09:57:02
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