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f-x-y-f-2x-2y-2y-2x-IF-f-2-x-0-f-2-x-k-0-Find-minimum-value-of-k-gt-0-




Question Number 9030 by Nemish Zawar last updated on 15/Nov/16
f(x ,y)=f(2x+2y, 2y−2x)  IF f(2^x ,0)=f(2^(x+k) ,0)  Find minimum value of k>0.
$${f}\left({x}\:,{y}\right)={f}\left(\mathrm{2}{x}+\mathrm{2}{y},\:\mathrm{2}{y}−\mathrm{2}{x}\right) \\ $$$$\mathrm{I}{F}\:{f}\left(\mathrm{2}^{{x}} ,\mathrm{0}\right)={f}\left(\mathrm{2}^{{x}+{k}} ,\mathrm{0}\right) \\ $$$$\boldsymbol{\mathrm{F}}\mathrm{ind}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}>\mathrm{0}. \\ $$

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