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If a^2+b^2+c^2=16 and a b+b c+c a=10 , f...

If `a^2+b^2+c^2=16` and `a b+b c+c a=10` , find the value of `a+b+c`

Text Solution

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Given:
`ab+bc+ca=10`
`a^2+b^2+c^2=16`
`(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)`
`=>(a+b+c)^2=16+2(10)`
`=>a+b+c=sqrt(16+20)`
`=>a+b+c=sqrt36=6`
`therefore a+b+c=6`
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