If $a + b + c = 9$ and $ab + bc + ca = 23$, find $a^{2} + b^{2} + c^{2}$.

Question

Aicharya · Accepted Answer

$(a+b+c)^{2} = a^{2}+b^{2}+c^{2} + 2(ab+bc+ca) \Rightarrow 81 = (a^{2}+b^{2}+c^{2}) + 46 \Rightarrow a^{2}+b^{2}+c^{2} = 35$.

Solution