Question

if A sq+B sq+C sq =20 and a+b+c= 0.find ab+bc+ca

Answer 1

(a+b+c)^2 =0
a^2 + b^2 + c^2 + 2ab + 2bc + 2ca =0
20 +2ab + 2bc + 2ca =0
2ab + 2bc + 2ca = -20
ab + bc + ca = -20/2 => -10

Answer 2

AnswEr:

We have,

$\quad\sf \: (a + b + c) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ \\ \implies \sf \: {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ \\ \implies \sf \: {0}^{2} = 20 + 2(ab + bc + ca) \\ \\ \implies \sf \: - 20 = 2(ab + bc + ca) \\ \\ \implies \sf \frac{ - 20}{2} = \frac{2(ab + bc + ca)}{2} \\ \\ \implies \sf \: - 10 = ab + bc + ca \\ \\ \implies \sf \: ab + bc + ca = - 10$

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