Answered: Please show step-by-step solution

Name: Please show step-by-step solution
Uploaded: 2024-03-20T06:46:03.000Z
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Description: Please show step-by-step solution

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Please show step-by-step solution

Expert Solution

Step 1

(3)

Given information: $4 x^{3} = 2 x^{- 1}$

To simplify the equation use the operations division and multiplication.

The equation can be written as, $4 x^{3} = \frac{2}{x}$

First of all Multiply by x on both the sides,

$\begin{array}{rcl} (4 x^{3}) x & = & (\frac{2}{x}) x \\ 4 x^{4} & = & 2 \end{array}$

Step 2

Divide by 4 on both the sides,

$\begin{array}{rcl} \frac{4 x^{4}}{4} & = & \frac{2}{4} \\ x^{4} & = & \frac{1}{2} \end{array}$

It is a degree of 4, to simplify this substitute $t = x^{2}$ and $t^{2} = x^{4}$

$t = \sqrt{\frac{1}{2}}, t = - \sqrt{\frac{1}{2}}$

and substitute back $t = x^{2}$

$x^{2} = \sqrt{\frac{1}{2}}, x^{2} = - \sqrt{\frac{1}{2}}$

On solving both, the solution is,

$x = \sqrt[4]{\frac{1}{2}}, x = - \sqrt[4]{\frac{1}{2}} a n d x = i (\sqrt[4]{\frac{1}{2}}), x = - i (\sqrt[4]{\frac{1}{2}})$

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