How would you simplify √2x+3−√x+1=1?

1 Answer
Noah G
Feb 9, 2016

You must mean how to solve. I'll solve the equation for you.

Explanation:

√2x+3−√x+1=1

√2x+3=1+√x+1

(√2x+3)2=(1+√x+1)2

2x+3=1+2√x+1+x+1

2x−x+3−1−1=2√x+1

x+1=2√x+1

(x+1)2=(2√x+1)2

x2+2x+1=4(x+1)

x2+2x+1=4x+4

x2+2x−4x+1−4=0

x2−2x−3=0

(x−3)(x+1)=0

x=3andx=−1

Always check the solutions in the original equation to make sure they aren't extraneous. If they do not work in the original equation, you must reject them.

√2×3+3−√3+1=1

So, x = 3 works. Now, let's check x = -1:

√2×−1+3−√−1+1=1

So, x = -1 works as well.

Your solution set would be x = 3, -1

Practice exercises:

  1. Solve for x.

a) √3x−2−√x−2=2

b) √4x+5+√8x+9=12

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