Скоротіть дріб [tex]\frac{\sqrt{x} -9}{\sqrt[4]{x} -3}[/tex]. Created by dimaonopko2020. algebra-ru

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dimaonopko2020 @dimaonopko2020

July 2022 2 6 Report

Скоротіть дріб [tex]\frac{\sqrt{x} -9}{\sqrt[4]{x} -3}[/tex]

ZlataSergeeva2000

Ответ:

$\star \ \ \ \displaystyle \sqrt[4]{x}=x^{\frac{1}{4}}\ \ \Rightarrow \ \ \ \sqrt{x}=x^{\frac{1}{2}}=x^{\frac{1}{4}\cdot 2}=(x^{\frac{1}{4}})^2=(\sqrt[4]{x})^2\ \ \star \\\\\\\frac{\sqrt{x}-9}{\sqrt[4]{x}-3}=\frac{(\sqrt[4]{x})^2-3^2}{\sqrt[4]{x}-3}=\frac{(\sqrt[4]{x}-3)(\sqrt[4]{x}+3)}{\sqrt[4]{x}-3}=\sqrt[4]{x}+3$

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NNNLLL54

Verified answer

Решение:

$\dfrac{\sqrt{x} -9}{\sqrt[4]{x} -3} = \dfrac{(\sqrt[4]{x} )^2 -3^2}{\sqrt[4]{x} -3} = \dfrac{(\sqrt[4]{x} -3)(\sqrt[4]{x} +3)}{\sqrt[4]{x} -3} = \sqrt[4]{x} +3$

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