Question

if a^2 + b^ 2 + c ^2= 20 and a+ b+ c = 0 find an+bc+ca​

Answer 1

$We \:have \: a^{2} + b^{2} + c^{2} = 20 \:--(1) \\and \: a + b + c = 0 \: ---(2)$

/* On squaring equation (2), we get */

$(a+b+c)^{2} = 0$

$\implies a^{2} + b^{2} +c^{2} + 2ab + 2bc+2ca = 0$

$\implies (a^{2} + b^{2} +c^{2} )+ 2(ab + bc+ca) = 0$

$\implies 20 + 2(ab + bc+ca) = 0\: [From \:(1)]$

$\implies 2(ab + bc+ca) = -20$

$\implies ab + bc+ca= \frac{-20}{2}$

$\implies ab + bc+ca= -10$

Therefore.,

$\red{ Value \: of \: ab + bc+ca}\green {= -10}$

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