MHB How can I solve radical equations using the given hint?

[mathdad]

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?

 

[joypav]

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.

 

[mathdad]

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.