Solve the equation.\sqrt[3]{x}=2\sqrt[4]{x}

nagasenaz 2021-09-27 Answered

Solve the equation.
\(\sqrt[3]{x}=2\sqrt[4]{x}\)

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Expert Answer

Maciej Morrow
Answered 2021-09-28 Author has 13549 answers

Step 1
Given: \(\sqrt[3]{x}=2\sqrt[4]{x}\)
For finding solution of given equation, we take power 12 both side and simplify it
Step 2
So,
\({\sqrt[3]{x}}^{12}=2\sqrt[4]{x}^{12}\)
\(\displaystyle{x}^{{{4}}}={2}^{{{12}}}{x}^{{{3}}}\)
\(\displaystyle{x}^{{{4}}}-{2}^{{{12}}}{x}^{{{3}}}={0}\)
\(\displaystyle{x}^{{{3}}}{\left({x}-{2}^{{{12}}}\right)}={0}\)
\(\displaystyle{x}={0},{2}^{{{12}}}\)
Hence, solution of given equation is \(\displaystyle{x}={0},{2}^{{{12}}}\).

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