Question

If a,b, and c are non-zero reals such that a + b + c = 11, and 1/a + 1/b + 1/c = 0, what is the value of a^2 + b^2 + c^2?

Answer 1

1/a + 1/b + 1/c = 0

bc+ac+ab = 0

a^2 + b^2 + c^2
=(a+b+c)^2 -2(ab+bc+ac)
=(11)^2-2(0)
=121