SOLUTION: My maths teacher gave the whole class this really..interesting question: The reciprocal of which number is the same as the original number, subtract one. Prove it! I am havin

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Question 913200: My maths teacher gave the whole class this really..interesting question:
The reciprocal of which number is the same as the original number, subtract one. Prove it!
I am having a hard time fully understanding the question, but what I do understand is that a to get the reciprocal of a number, you simply divide it by one. That's as far as I have gotten.
I really need this because I could get 49% on my next assessment. If you could also explain how you worked it out, that would be absolutely amazing!
Thank You SO MUCH!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
let x = unknown number


x = original number
1/x = reciprocal of original number

"The reciprocal of which number is the same as the original number, subtract one." translates to 1%2Fx+=+x-1

1%2Fx+=+x-1

1+=+x%2A%28x-1%29

1+=+x%5E2-x

0+=+x%5E2-x-1

x%5E2-x-1=0

Use the quadratic formula to solve for x

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%28-1%29%2B-sqrt%28%28-1%29%5E2-4%281%29%28-1%29%29%29%2F%282%281%29%29 Plug in a+=+1, b+=+-1, c+=+-1

x+=+%281%2B-sqrt%281-%28-4%29%29%29%2F%282%29

x+=+%281%2B-sqrt%281%2B4%29%29%2F%282%29

x+=+%281%2B-sqrt%285%29%29%2F2

x+=+%281%2Bsqrt%285%29%29%2F2 or x+=+%281-sqrt%285%29%29%2F2

x+=+1.618034 or x+=+-0.618034 Use a calculator to evaluate the expressions

So the number is either x+=+1.618034 or x+=+-0.618034

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim