Marc solves the equation Latex: (\sqrt[4]{x})^3=5\textsf{.} His work is shown below. Step 1: Latex: (\sqrt[4]{x})^3=5 ( √ [ 4 ] x ) 3 = 5 Step 2: Latex: x^{\frac{3}{4} }=5 x 3 4 = 5 Step 3: Latex: x^{\frac{3}{4} \cdot \frac{4}{3} }=5^{\frac{4}{3} } x 3 4 ⋅ 4 3 = 5 4 3 Step 4: Latex: x=\sqrt[3]{5 \cdot 5 \cdot 5 \cdot 5} x = √ [ 3 ] 5 ⋅ 5 ⋅ 5 ⋅ 5 Step 5: Latex: x=5\sqrt[3]{\not{5} \cdot \not{5} \cdot\not {5} \cdot 5} x = 5 √ [ 3 ] ¬ 5 ⋅ ¬ 5 ⋅ ¬ 5 ⋅ 5 Step 6: Latex: x=5\sqrt[3]{5} x = 5 √ [ 3 ] 5 Explain what Marc did in steps 4 and 5. Why did he do this? Create your own radical equation and explain how to solve it. Is there an extraneous solution to your equation?

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abidemiokin abidemiokin · Answer 1 · 2021-11-02T11:41:31+01:00

Based on the calculation, we can say that there is an extraneous solution to the equation

Given the equation solved by Marc expressed as:

[tex](\sqrt[4]{x})^3=5[/tex]

We are to check if the indices equation has an extraneous equation.

According to the law of indices [tex](\sqrt[n]{m} )^a=m^{\frac{a}{n} }[/tex], the expression becomes:

[tex](\sqrt[4]{x})^3=5\\x^\frac{3}{4}=5\\[/tex]

Raise both sides to the power of 4/3 as shown:

[tex](x^\frac{3}{4} )^\frac{4}{3} = 5^\frac{4}{3}\\x^1 = 5^\frac{4}{3}\\x = 5^\frac{4}{3}\\[/tex]

This shows that there is an extraneous solution to the equation

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