   Chapter 0.6, Problem 3E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The solution of the equation x44x2=4.

Explanation

Given information:

The equation, x44x2=4.

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.

Calculation:

Consider the expression,

x44x2=4

Rewrite the expression as,

x44x2+4=0

The left side expression is x44x2+4.

The above expression can be written as,

(x2)24x2+4

Substitute x2=y in the above expression,

y24y+4

Factor of y2 are (y)(y).

The factors of 4 are (1)(4),(2)(2),(1)(4)and(2)(2).

Consider the factors (y)(y) and (1)(4)

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

What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 6372, evaluate the expression. 68. 1+22

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

For f(x) = 5 + g(x), f(x) = _____. a) 5g(x) b) 5 + g(x) c) 0 g(x) d) g(x)

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