Question

If a + b + c = 6 , ${a^2} + {b^2} + {c^2} = 26$ , then what is ab + bc + ca equal to ?
A.0
B.2
C.4
D.5

Answer 1

 Hint-Square a + b + c = 6 on both sides and use the formula of ${\left( {a + b + c} \right)^2}$. Put the given value from the question to find the value of the desired answer .

Complete step-by-step answer:
According to the question,
a + b + c = 6
On squaring both sides,
${\left( {a + b + c} \right)^2} = {6^2}$
$ \Rightarrow {a^2} + {b^2} + {c^2} + 2\left( {ab + bc + ca} \right) = 36$ ( since ${\left( {a + b + c} \right)^2} = {a^2} + {b^2} + {c^2} + 2\left( {ab + bc + ca} \right)$ )
Using the value of ${a^2} + {b^2} + {c^2} = 26$ from the given information
$ \Rightarrow 26 + 2\left( {ab + bc + ca} \right) = 36$
\[ \Rightarrow 2\left( {ab + bc + ca} \right) = 10\]
$ \Rightarrow ab + bc + ca = 5$
Note-In such types of questions we need to recall the formula and step by step use the given information accurately. Remember to state the complete formula while solving such questions.