Chapter 9: Q.461. (page 984)

Solve the given equation.
$x^{\frac{2}{3}} - 10^{\frac{1}{3}} + 24 = 0$

Short Answer

Expert verified

The solutions are $x = 64$ and $x = 216$ .

Step by step solution

Step 1. Given information.

The given equation is $x^{\frac{2}{3}} - 10^{\frac{1}{3}} + 24 = 0$ .

Step 2. Simplify the equation.

$\begin{array}{rcl} x^{\frac{2}{3}} - 10 x^{\frac{1}{3}} + 24 & = & 0 \\ {(x^{\frac{1}{3}})}^{2} - 10 x^{\frac{1}{3}} + 24 & = & 0 \\ {(x^{\frac{1}{3}})}^{2} - 6 x^{\frac{1}{3}} - 4 x^{\frac{1}{3}} + 24 & = & 0 \\ x^{\frac{1}{3}} (x^{\frac{1}{3}} - 6) - 4 (x^{\frac{1}{3}} - 6) & = & 0 \\ (x^{\frac{1}{3}} - 4) (x^{\frac{1}{3}} - 6) & = & 0 \end{array}$

Step 3. Solve the equation for x.

$\begin{array}{rcl} x^{\frac{1}{3}} - 6 & = & 0 \\ x^{\frac{1}{3}} & = & 6 \\ {(x^{\frac{1}{3}})}^{3} & = & 6^{3} \\ x & = & 216 \end{array}$ and $\begin{array}{rcl} x^{\frac{1}{3}} - 4 & = & 0 \\ x^{\frac{1}{3}} & = & 4 \\ {(x^{\frac{1}{3}})}^{3} & = & 4^{3} \\ x & = & 64 \end{array}$

Step 4. Simplified answer.

Hence, the required solutions are $x = 64$ and $x = 216$ .

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Solve the given equation.
$x^{\frac{2}{3}} - 10^{\frac{1}{3}} + 24 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

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Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Solve the given equation.
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