SOLUTION: When verifying an identity, why can't you square both sides?

Question 594645: When verifying an identity, why can't you square both sides?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Squaring both sides essentially weakens a statement. For example, suppose that

Squaring both sides yields

However the second equation is not equivalent to the first one, as x could equal 1 or -1. You can square both sides when dealing with "if and only if" relations, for example, if you know that x must be positive.
RELATED QUESTIONS
In proving a trig identity, why is working only one side important? Can you provide an... (answered by josgarithmetic)

when you mutiply or divide by both sides of an inequatity why does the symbol... (answered by vleith)

How do i verify an identity? I am very confused on the process of verifying... (answered by Fombitz)

Could you give me an example of why the inequality sign changes when both sides are... (answered by Fombitz)

Could you give me an example of why the inequality sign changes when both sides are... (answered by Mathtut)

Solve the given equation: sin t − 1 = cos t? I have to find an identity that... (answered by josgarithmetic)

Why the inequality sign changes when both sides are multiplied or divided by a negatie... (answered by )

Why does the inequality sign change when both sides are multiplied or divided by a... (answered by stanbon)

He all, can you please help me verifying this identity step by step?:... (answered by ikleyn)