Question

ПОМОГИТЕ!!!!
Найдите $frac{g(4-x)}{g(4+x)}$, если $g(x)=sqrt[7]{x(8-x)}$ , при IxI≠4

Answer 1

$displaystyle g(x)=sqrt[7]{x(8-x)}\\frac{g(4-x)}{g(4+x)}=frac{sqrt[7]{(4-x)(8-(4-x))}}{sqrt[7]{(4+x)(8-(4+x))}}=sqrt[7]{frac{(4-x)(8-4+x)}{(4+x)(8-4-x)}}=\\\=sqrt[7]{frac{(4-x)(4+x)}{(4+x)(4-x)}}=sqrt[7]{1}=boxed{1}$

Answer 2

спасибо