Inspired by Nihar Mahajan

Algebra Level 2

ac>bc \Large \color{#D61F06}{a}^{\color{#20A900}{c}} > \color{#3D99F6}{b}^{\color{#20A900}{c}}

Given that a,\color{#D61F06}{a}, b,\color{#3D99F6}{b}, and c\color{#20A900}{c} are real numbers such that

  • ab>0\color{#D61F06}{a} \color{#3D99F6}{b} > 0.
  • c>0 \color{#20A900}{c} > 0 .
  • c \color{#20A900}{c} is not an even integer.
  • a>b \color{#D61F06}{a} > \color{#3D99F6}{b} .

What can be said about the very first statement above?


Inspiration.

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