How can I solve radical equations using the given hint?

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The discussion focuses on solving the radical equation sqrt{x^4 - 13x^2 + 37} = 1 by applying the hint provided in the textbook, which suggests substituting x^2 with t and x^4 with t^2. Participants confirm that after substituting, the next steps involve squaring both sides of the equation, subtracting 1, and factoring the resulting expression. Emphasis is placed on the necessity of back-substituting to find the original variable solutions and the importance of verifying answers in radical equations to ensure accuracy.

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Determine all of the real number solutions for the radical equation.

sqrt {x^4 - 13x^2 + 37} = 1

Hint given in textbook:

Let x^2 = t and x^4 = t^2

After applying the hint given, do I proceed as usual by squaring both sides?

I have to back-substitute somewhere in the solution steps, right?

Why is it important to always check the answer (s) when dealing with radical equations?
 
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Yes, it is solving as usual.
You can square both sides, then subtract 1 from both sides.
Factor as usual. Substitute back in.

Try it out and see if you get the correct answers.
 
joypav said:
Yes, it is solving as usual.
You can square both sides, then subtract 1 from both sides.
Factor as usual. Substitute back in.

Try it out and see if you get the correct answers.

Great. Ok. It's not so bad.
 

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