Algebra and Surds!

**Mirage** · Aug 4th 2010, 07:43 PM

Find the exact value of

x² + 1/x²

if x = 1 + 2 * square root of 3 / 1 - 2 * square root of 3

Answer: 434/121 = 3 71/121

**Mirage** · Aug 4th 2010, 07:44 PM

Does anyone end up with this answer?? Pls help! I dnt kno whether it's a printing error in the textbook or I just cnt solve it

**Also sprach Zarathustra** · Aug 4th 2010, 07:48 PM

Originally Posted by Mirage

Does anyone end up with this answer?? Pls help! I dnt kno whether it's a printing error in the textbook or I just cnt solve it

Answer: 434/121 = 3 71/121

Your answer is correct!

**Mirage** · Aug 4th 2010, 07:52 PM

Thanks for your response

I don't know how to arrive at that answer. Would you be able to type out your working out pls?

**pickslides** · Aug 4th 2010, 08:02 PM

Would be more helpful if you used some brackets, is this the question? find $\frac{x^2+1}{x^2}$ where $x = \frac{1+2\sqrt{3}}{1-2\sqrt{3}}$

**Mirage** · Aug 4th 2010, 08:08 PM

It is x² + (1/x²)
second part is correct

Sorry, I'm new to this. How do you type maths? Is there some sort of program that you use?

**pickslides** · Aug 4th 2010, 08:14 PM

Originally Posted by Mirage

Sorry, I'm new to this. How do you type maths? Is there some sort of program that you use?

**pickslides** · Aug 4th 2010, 08:16 PM

Originally Posted by Mirage

It is x² + (1/x²)

$(\frac{1+2\sqrt{3}}{1-2\sqrt{3}})^2+\frac{1}{(\frac{1+2\sqrt{3}}{1-2\sqrt{3}})^2}$

Start expanding brackets.

**Also sprach Zarathustra** · Aug 4th 2010, 08:25 PM

You also can find x+1/x=2cos(t) (much easier )

and then x^2+(1/x^2)=2cos(2t)

**pickslides** · Aug 4th 2010, 08:28 PM

Originally Posted by Also sprach Zarathustra

You also can find x+1/x=2cos(t) (much easier )

and then x^2+(1/x^2)=2cos(2t)

Good advice ASZ, although remember this is in a pre-uni level forum.

Thread: Algebra and Surds!