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प्रश्न
If a2 + b2 + c2 = 20 and a + b + c = 0, find ab + bc + ca.
उत्तर
Recall the formula
`(a+b+c)^2 = a^+b^2 +c^2 +2(ab +bc +ca)`
Given that
`a^2 +b^2 +c^2 = 20`
`(a+b+c) = 0`
Then we have
`(a+b+c)^2 = a^2 +b^2 +c^2 +2 (ab +bc + ca)`
`(0)^2 = 20 +2(ab +bc + ca)`
` 20+2(ab +bc + ca) = 0`
`2(ab + bc + ca) = -20`
`(ab +bc + ca) = -10`
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