Why do I get incorrect solutions x=0 and x=2 for

treetopssan

treetopssan

Answered question

2022-01-30

Why do I get incorrect solutions x=0 and x=2 for x+1+4x+1=0?

Answer & Explanation

basgrwthej

basgrwthej

Beginner2022-01-31Added 13 answers

Step 1
Here is one correct way to solve this problem I learnt from comments.
I should write
x+1=4x+1
{(x+1)2=4x+1(x+1)0
{x(x2)=0x1
Then I should solve x(x2)=0 to get x=0 and x=2. Then I should reject both solutions because both solutions do not satisfy x1. Therefore the equation has no solutions.
Karly Logan

Karly Logan

Beginner2022-02-01Added 11 answers

Step 1
You can easily track where the extra solutions were introduced
x+1+4x+1=00+1+1=0
x+1=4x+10+1=0+1
x2+2x+1=4x+10+0+1=0+1
x22x=000=0
x(x2)=00(02)=0
Repeat with x=2.
If you turn a=b to a2=b2, you also allow a=b.

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