If t^2 = x can't I just replace t^2 with x?

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You can replace t^2 with x in the equation t^2 = x, as both expressions represent the same value. This substitution is valid unless specified otherwise in a particular problem. For instance, t^6 can be expressed as (t^2)^3, which simplifies to x^3. However, it's important to note that taking the square root of both sides results in |t| = √x, indicating that t can be either √x or -√x. The discussion highlights the flexibility of variable substitution in algebraic expressions.
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Rather than having to take the root of t? It doesn't seem like there's a rule against it, unless it is for a specific problem.
 
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The statement ##t^2=x## is saying that the expressions (strings of text) ##t^2## and ##x## represent the same number. So yes, you can certainly replace one with the other. For example if you're asked what ##t^6## is, you can write ##t^6=(t^2)^3=x^3##.

But I'm not sure what exactly you have in mind. Perhaps you can clarify. Is there a specific problem where someone has told you that you can't replace ##t^2## with ##x##?

Note by the way that if you take the square root of both sides, you get ##|t|=\sqrt{x}##, not ##t=\sqrt{x}##. The statement ##t^2=x## implies that either ##t=\sqrt{x}## or ##t=-\sqrt{x}##.
 
No no specific problem, I was just trying to make my life a bit easier.
 

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