Question

ifa2+b2+c2 =280 and ab+bc+ca=9/2,then find the value of (a+b+c)3.is the given Q. CORRECT?

Answer 1

given that,
${a}^{2} + {b}^{2} + {c}^{2} = 280 \: ..........(1)$

and,
$ab + bc + ca = \frac{9}{2} \\ therefore \\ 2ab + 2bc + 2ca = 9 \: ................(2)$
Adding equations 1 and 2,
$2ab + 2bc + 2ca + {a}^{2} + {b}^{2} + {c}^{2}= 9 + 280 \\ therefore \\ {(a + b + c)}^{2} = 289 \\ \implies \: a + b + c = \pm17$
so,
${(a + b + c)}^{3} = { ( \pm17)}^{3} \\ \implies {(a + b + c)}^{3} = \pm \: 4913$
Yes the question is correct.

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