   Chapter 0.5, Problem 25E

Chapter
Section
Textbook Problem

By any method, determine all possible real solutions of each equation in Exercises 13–30. Check your answers by substitution. x = 2 − 1 x

To determine

To calculate: The all real solutions in the quadratic equation x=21x.

Explanation

Given Information:

The provided quadratic equation is x=21x.

Formula used:

The value of x in the equation ax2+bx+c=0 can be given by the quadratic formula,

x=b±b24ac2a where a,b and c are real numbers with a0.

Calculation:

Consider the quadratic equation x=21x.

Since the denominator of the equation are 1,1,x therefore, the L.C.M of denominator is x.

Multiply by x on both sides in the above equation,

xx=2x1xxx2=2x1

Add 2x+1 on both sides,

x22x+1=2x12x+1x22x+1=0

Compare the above equation with the equation ax2+bx+c=0,

a=1, b=2 and c=1

Put the values of a,b,c in the quadratic formula x=b±b24ac2a

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