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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 Another Way | Comment 2 of 3 |
2(a^2+b^2) =  (a+b)^2 + (a-b)^2
or, 2*25 = 1^2+ (a-b)^2
or, (a-b)^2 = 50-1=49

Again,
2(a^4+b^4) =  (a^2+b^2)^2 + (a^2-b^2)^2
or, 2(a^4+b^4) = 25^2 + 49 = 674
or, a^4+b^4 = 674/2 = 337
  Posted by K Sengupta on 2016-07-13 01:27:16
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