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Prove that p x^(q-r)+q x^(r-p)+r x^(p-q)...

Prove that `p x^(q-r)+q x^(r-p)+r x^(p-q)> p+q+r ,where p, q, r` are distinct and `x!=1.`

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We know that
Weighted A.M. `gt ` weighted G.M.
` rArr (px^(q-r)+qx^(r-p)+rx^(p-q))/(p+q+r) gt [(x^(q-r))^p(x^(r-p))^q(x^(p-q))^r]^((1)/(p+q+r))`
or ` (px^(q-r)+qx^(r-p)+rx^(p-q))/(p+q+r)gt 1`
or ` px^(q-r)+qx^(r-p)+rx^(p-q) gt p+q+r`
In case either `p=q=r or x=1`, inequality becomes equality.
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