Given a+b=1 & a^2+b^2 =25,
Find a^4+b^4, without solving for a and b.
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=6252(ab)^2
a^4+b^4=6252(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 20151118 08:33:17 