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Prove that a^p b & q >((a p+b p)/(p+q))^...

Prove that `a^p b & q >((a p+b p)/(p+q))^(p+q)dot`

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Consider p quantities each point equal to a and q quantities each equal to b. we know that
` A.M. gt G.M. `
`therefore ((a+a+....." to p terms")+(b+b+...."to q terms"))/(p+q)`
` gt [(caxxa.... " to p factors ")(bxxb....."to q factors ")]^((1)/(p+q))`
` rArr (ap+bq)/(p+q)gt (a^pb^q)^((1)/(p+q))`
` rArr ((ap+bq)/(p+q))^(p+q) gt (a^pb^q)` lt
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