Question

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

Answer 1

refer the pic
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Answer 2

Heya,

Given,
${a}^{2} + {b}^{2} + {c}^{2} = 20 \\ a + b + c = 0$

Now,
${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ {(0)}^{2} = 20 + 2(ab + bc + ca) \\ 0 - 20 = 2(ab + bc + ca) \\ \frac{ - 20}{2} = ab + bc + ca \\ - 10 = ab + bc + ca$

Hence,
ab + bc + ca = -10

Hope it helps you.