   Chapter 0.6, Problem 10E

Chapter
Section
Textbook Problem

Solve the equations in Exercises 1–26. ( x 2 + 1 ) x + 1 − ( x + 1 ) 3 = 0

To determine

To calculate: The solution of the equation (x2+1)x+1(x+1)3=0.

Explanation

Given information:

The equation, (x2+1)x+1(x+1)3=0.

Formula used:

Zero product property,

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

Calculation:

Consider the expression,

(x2+1)x+1(x+1)3=0

The left side expression is (x2+1)x+1(x+1)3.

As both the term contains the term x+1. Thus, the common factor is x+1.

Now, factor out the common factor and simplify as below,

(x2+1)x+1(x+1)3=x+1(x2+1(x+1)2)=x+1(x2+1(x+1))=x+1(x2+1x1)=x+1(x2x)

Now, consider the term (x2x)

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