If ( a + b + c) = 0 and ab + bc + ca = -11, then what is the value of $a^2 +b^2 +c^2$.

22

If ( a + b + c) = 0

ab + bc + ca = -11

Find the value of $a^2 +b^2 +c^2$

If the number of equations are less than the number of variables then we can put the extra variables according to our choice = 

So here two equations given and three variables are present so put c = 0

If ( a + b) = 0

ab  = -11

find the value of $a^2 +b^2 $ = ?

( a + b )² = a² + b² + 2ab

( 0)² = a² + b² + 2(-11)

0 = a² + b² -22

a² + b² = 22