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lf abcd=1 where a,b,c,d are positive re...

lf `abcd=1` where a,b,c,d are positive reals then the minimum value of `a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd` is

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The correct Answer is:
10
Given,abcd `=1`
We know that , `AM ge GM`
`therefore (a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd)/(10)`
`ge [a^2xxb^2xxc^2xxd^2xx(ab)xx(ac)xx(ad)xx(bc)xx(bd)xx(cd)]^(1//10)`
`=(a^5xxb^5xxc^5xxd^5)^(1//10)`
`=(abcd)^(1//2)`
`=(1)^(1//2)`
`rArr (a^2b^2+c^2+d^2+ab+ac+ad+bc+bd+cd)/(10) ge 1`
`rArr a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd +cd ge 10`.
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