Chapter 11: Q.181 (page 1069)

In the following exercises, solve equations in Quadratic Form for $x^{\frac{2}{3}} + 4 x^{\frac{1}{3}} = 12$ .

Short Answer

Expert verified

The solution of the quadratic equation is $x = 8, x = - 216$ .

Step by step solution

Step 1. Given Information.

The given equation is $x^{\frac{2}{3}} + 4 x^{\frac{1}{3}} = 12$ .

Step 2. Simplifying .

Simplify $x^{\frac{2}{3}} + 4 x^{\frac{1}{3}} = 12$

${(x^{\frac{1}{3}})}^{2} + 4 x^{\frac{1}{3}} = 12$

Substitute $u = x^{\frac{1}{3}}$ , we get:-

$u^{2} + 4 u = 12$

$u^{2} + 4 u - 12 = 0$

Step 3. Solving quadratic equation .

By using the quadratic formula:-

$u^{2} + 4 u - 12 = 0$

$u_{1, 2} = \frac{- 4 \pm \sqrt{4^{2} - 4 \cdot 1 \cdot (- 12)}}{2 \cdot 1} u_{1, 2} = \frac{- 4 \pm 8}{2 \cdot 1} u_{1} = \frac{- 4 + 8}{2 \cdot 1}, u_{2} = \frac{- 4 - 8}{2 \cdot 1} u = 2, u = - 6$

Step 4. Simplifying .

Solve for $\begin{array}{rcl} x^{\frac{1}{3}} & = & 2; x = 8 \\ x^{\frac{1}{3}} & = & - 6; x = - 216 \end{array}$

Therefore, The solution is $x = 8, x = - 216$ .

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In the following exercises, solve equations in Quadratic Form for $x^{\frac{2}{3}} + 4 x^{\frac{1}{3}} = 12$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplifying .

Step 3. Solving quadratic equation .

Step 4. Simplifying .

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In the following exercises, solve equations in Quadratic Form for x23 + 4x13 = 12.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplifying .

Step 3. Solving quadratic equation .

Step 4. Simplifying .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve equations in Quadratic Form for $x^{\frac{2}{3}} + 4 x^{\frac{1}{3}} = 12$ .