   Chapter 0.6, Problem 4E

Chapter
Section
Textbook Problem

Solve the equations in Exercises 1–26. x 4 − x 2 = 6

To determine

To calculate: The solution of the equation x4x2=6.

Explanation

Given information:

The equation, x4x2=6.

Formula used:

Steps to calculate the factors of quadratic equation ax2+bx+c by trial and error method,

Step1: Factor ax2 as (a1x)(a2x) with a1 positive.

Step2: Factor c as c1c2.

Step 3: Check if ax2+bx+c=(a1x±c1)(a2x±c2)

If yes, then (a1x±c1)(a2x±c2) are the factors.

Step 4: If not, try other factorization of ax2 and c and repeat all the steps.

The distributive law,

(a±b)c=ac±bc

Where, a, b and c are any real numbers.

Zero product property,

If a product of two number is zero, one of the two must be zero.

Calculation:

Consider the expression,

x4x2=6

Rewrite the expression as,

x4x26=0

The left side expression is x4x26.

The above expression can be written as,

(x2)2x26

Substitute x2=y in the above expression,

y2y6

Factor of y2 are (y)(y).

The factors of 6 are (1)(6),(2)(3),(2)(3)and(1)(6).

Consider the factors (y)(y) and (1)(6).

Now,

(y+1)(y6)=y(y6)+1(y6)=y26y+y6=y25y6

Which is not the original expression

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Other Equations Find all real solutions of the equation. 112. x5x+6=0

Precalculus: Mathematics for Calculus (Standalone Book)

Calculate y'. 46. y=ln|x242x+5|

Single Variable Calculus: Early Transcendentals, Volume I

A population of N = 15 scores has SX = 120. What is the population mean?

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the integral. 25. 4xx3+x2+x+1dx

Single Variable Calculus: Early Transcendentals

True or False: xy + 6x2y = 10 x3 is linear.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 