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

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

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