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Chapter 9: Q. 9.157 (page 1098)

Solve:x-2+2=x.

Short Answer

Expert verified

The solution isx=2,3.

Step by step solution

01

Step 1. Given Information  

We are given the quadratic equation x-2+2=xand we need to solve it.

02

Step 2. Finding the solution  

Isolating the radical on one side of the equation:

x-2+2=x鈬�x-2+2-2=x-2鈬�x-2=x-2

Squaring both sides of the equation, we get:

x-22=x-22鈬�x-2=x2-4x+4鈬�x2-4x+4-x+2=0鈬�x2-5x+6=0鈬�x2-2x-3x+6=0鈬�xx-2-3x-2=0鈬�x-3x-2=0

Using the zero product property, we get:

x-2=0鈬�x=2x-3=0鈬�x=3

03

Step 3. Checking the answer  

x=2,x-2+2=x鈬�2-2+2=2鈬�0+2=2鈬�2=2x=3,3-2+2=3鈬�1+2=3鈬�1+2=3鈬�3=3

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