Пусть ab в четвертой степени. Created by enjdh. algebra-ru

Пусть ab в четв...

enjdh @enjdh

August 2022 1 9 Report

Пусть a<b и оба числа отрицательны. Доказать, что а в четвертой >b в четвертой степени

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FoundName

Verified answer

$a\ \textless \ b; a\ \textless \ 0, b\ \textless \ 0\\
|a|=|-a|, |b|=|-b|\\
|a|\ \textgreater \ |b|\\
a^4=(-a)^4=(|a|)^4\\
b^4=(-b)^4=(|b|)^4$
Т.к. $|a|\ \textgreater \ |b|$ , то $(|a|)^4\ \textgreater \ (|b|)^4$

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