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If a^2+b^2+c^2=20 and a+b+c=0 , find a b...

If `a^2+b^2+c^2=20` and `a+b+c=0` , find `a b+b c+c a`

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1409003 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+ac)`
`2(ab+bc+ca)=-20`
`(ab+bc+ca)=-20/2`
`(ab+bc+ca)=-10`
`therefore (ab+bc+ca)=-10`
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