Question

If the sum of three integers is 10, then the sum of the fourth powers of the three integers cannot be less than A. 10000
B. 370
C. 418
D. 600

Answer 1

let the integers be a,b,c..
now we know (a^4 + b^4 + c^4)/3 >= cuberoot(a^4 b^4 c^4)
or a^4 + b^4 + c^4 >= 3abc cuberoot(abc)
and the equality holds when a=b=c
also a+b+c = 10
for equality,,we have a=b=c=10/3
hence min value is 3(10/3)^4 = 10000/27 = 370.something
so B should be the ans..