If a, b and c are non-zero reals such that a + b + c = 11 and \frac {1}{a} + \frac {1}{b} +\frac {1}{c} = 0, what is the value of a^2 + b^2 + c^2?
To find the value of a^2 + b^2 + c^2, we need to use the given equations and manipulate them to get the desired expression.
First, let's rewrite the second equation by finding their common denominator:
\frac {1}{a} + \frac {1}{b} +\frac {1}{c} = 0
Multiplying both sides by abc, we get:
bc + ac + ab = 0
Now, let's square both sides of the first equation:
(a + b + c)^2 = 11^2
a^2 + b^2 + c^2 + 2ab + 2ac + 2bc = 121
Since we know that ab + ac + bc = 0 from the second equation, we can express the equation above as:
a^2 + b^2 + c^2 + 2(0) = 121
a^2 + b^2 + c^2 = 121
Therefore, the value of a^2 + b^2 + c^2 is 121.