Question
If a + b + c = 26 and ab + bc + ca = 109, find the value of a2 + b2 + c2 = ?
Answer: Option A
$$\eqalign{
& {\left( {a + b + c} \right)^2} = {\text{ }}{a^2} + {b^2} + {c^2} + 2\left( {ab + bc + ca} \right) \cr
& \Rightarrow {\left( {26} \right)^2} = {\text{ }}{a^2} + {b^2} + {c^2} + 2\left( {109} \right) \cr
& \Rightarrow {a^2} + {b^2} + {c^2} = 676 - 218 \cr
& \Rightarrow {a^2} + {b^2} + {c^2} = 458 \cr} $$
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$$\eqalign{
& {\left( {a + b + c} \right)^2} = {\text{ }}{a^2} + {b^2} + {c^2} + 2\left( {ab + bc + ca} \right) \cr
& \Rightarrow {\left( {26} \right)^2} = {\text{ }}{a^2} + {b^2} + {c^2} + 2\left( {109} \right) \cr
& \Rightarrow {a^2} + {b^2} + {c^2} = 676 - 218 \cr
& \Rightarrow {a^2} + {b^2} + {c^2} = 458 \cr} $$
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