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## TeemoTheTerific Group Title help me on a question please... x= 1/2 +1/2sqrt5 show that... one year ago one year ago

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1. TeemoTheTerific Group Title

$x=\frac{ 1 }{ 2 } + \frac{ 1 }{ 2 }\sqrt{5}$

2. TeemoTheTerific Group Title

$\frac{ x^{2}+x ^{-2} }{ x-x ^{-1} }=3$

3. Azteck Group Title

$x=\frac{1}{2}+\frac{\sqrt{5}}{2}$ $x=\dfrac{1+\sqrt{5}}{2}$

4. enka Group Title

$x=\frac{1+\sqrt{5}}{2}\\ \frac{1}{x}=\frac{2}{1+\sqrt{5}}\times\frac{\sqrt{5}-1}{\sqrt{5}-1}=\frac{2\sqrt{5}-1}{4}=\frac{\sqrt{5}-1}{2}$ then $x-\frac{1}{x}=1\qquad(1)$ square both side to get: $x^2+\frac{1}{x^2}-2=1\\ x^2+\frac{1}{x^2}=3\qquad(3)$ now divide (3) by (1) to get the result

5. Azteck Group Title

$x^2+x^{-2}=3x-3x^{-1}$ Multiply both sides by x^2. $x^4+1=3x^3-3x$ $x^4-3x^3+3x+1=0$

6. TeemoTheTerific Group Title

i dont get it... both of you :P

7. TeemoTheTerific Group Title

yes ok

8. enka Group Title

first, we find the value of $x-\frac{1}{x}$

9. Azteck Group Title

You just sub in $\frac{1+\sqrt{5}}{2}$ into the original equation....

10. Azteck Group Title

And you prove that the LHS=RHS.

11. TeemoTheTerific Group Title

but no matter how manytimes i try i can never get it to equal 3

12. Azteck Group Title

Use a calculator if you can't do it....Use a calculator to solve the denominator first. You get one as the denominator...

13. Azteck Group Title

Jeez, you have a tool that can help you but you don't want to use it.

14. Azteck Group Title

You get 3 as the denominator when you plug the values into the numerator...

15. Azteck Group Title

numerator*

16. TeemoTheTerific Group Title

we need to show our working our using our skill of indices laws... But i dont have much

17. Azteck Group Title

There's no indice work when you learn that $x^{-1}=\frac{1}{x^1}$ $x^{-2}=\frac{1}{x^2}$

18. Azteck Group Title

Dude, now once you see the letter x, put that big fat fraction into your calculator and get your values...

19. Azteck Group Title

I can solve that by hand but that will take me ages, to write it on the computer, so no thank you...

20. enka Group Title

i hope it is can help you

21. enka Group Title

or this

22. TeemoTheTerific Group Title

thank you enka

23. enka Group Title

you're welcome :)