Question

If a^2+b^2+c^2=250 andvm ab+bc+ca=3 then find the value of a+b+c

Answer 1

$Given \: a^{2} + b^{2} + c^{2} = 250 \: ---(1)$

$and \: ab+bc+ ca = 3 \: --(2)$

$\underline{\blue { By \: algebraic \: identity :}}$

$\boxed { \pink { (a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca}}$

$\implies (a+b+c)^{2} \\= a^{2}+b^{2}+c^{2}+2(ab+bc+ca)\\= 250 + 2\times 3 \: [ From \:(1) \:and \:(2) ]\\= 250 + 6 \\= 256$

$Now, a + b + c = \pm \sqrt{256} \\= \pm 16$

Therefore.,

$\red{ Value \: of \: a + b + c }\green {=\pm 16 }$

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