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- Jun 16th 2012, 08:21 AMKalodaProving equations with radicals.
- Jun 16th 2012, 09:50 AMsimamuraRe: Proving equations with radicals.
We will need two formulas:

and

Let

Then we are given that

We need to show that .

Expand what we are given by first formula:

or

Since then

Now, equation can be rewritten as

Or

For simplicity, make substitution

Then we have that

There is only one real solution t=2, so

Finally,

That's all. - Jun 16th 2012, 11:09 AMrichard1234Re: Proving equations with radicals.
You're given

Let . Cubing both sides of this equation yields

, substitute with .

. Here, it helps to know that is. However, we know that . Squaring both sides of this equation yields

. Substitute into the previous equation to obtain

. Here it is evident that is a root (the other two roots are non-real). Hence we are done. - Jun 16th 2012, 11:30 AMKalodaRe: Proving equations with radicals.
Thank you VERY VERY MUCH!

- Jun 16th 2012, 12:37 PMbiffboyRe: Proving equations with radicals.