let-0-lt-p-lt-1-and-x-gt-0-prove-that-x-2-1-p-1-p-x-p-p-x-

Tinku Tara June 4, 2023 Vector 0 Comments

Question Number 92235 by ~blr237~ last updated on 05/May/20

let 0<p<1 and x>0 prove that x^2 ≤ (1−p)( ^((1−p)) (√x) ) +p (^p (√x))

$${let}\:\:\mathrm{0}<{p}<\mathrm{1}\:\:{and}\:\:{x}>\mathrm{0} \\ $$$${prove}\:{that}\:\:\:\:{x}^{\mathrm{2}} \leqslant\:\left(\mathrm{1}−{p}\right)\left(\:\:\:^{\left(\mathrm{1}−{p}\right)} \sqrt{{x}}\:\right)\:+{p}\:\left(\:^{{p}} \sqrt{{x}}\right) \\ $$$$ \\ $$$$ \\ $$

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