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# If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi

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Math Expert
Joined: 02 Sep 2009
Posts: 64939
If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi  [#permalink]

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04 Mar 2020, 01:31
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If x is a positive number and $$\frac{2}{1+\frac{2}{1+\frac{2}{1+...}}}=x$$, where the given expression extends to an infinite number of fractions, then what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

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Re: If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi  [#permalink]

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04 Mar 2020, 01:51
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1
1
$$\frac{2}{1+x} = x$$

x^2+x-2 = 0

(x+2)(x-1)=0

x=1 (Disregard the negative one)

Bunuel wrote:
If x is a positive number and $$\frac{2}{1+\frac{2}{1+\frac{2}{1+...}}}=x$$, where the given expression extends to an infinite number of fractions, then what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

Project PS Butler

Are You Up For the Challenge: 700 Level Questions
Director
Joined: 25 Jul 2018
Posts: 731
If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi  [#permalink]

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04 Mar 2020, 01:54
1
1
If x is a positive number and $$\frac{2}{1+\frac{2}{1+\frac{2}{1+...}}}=x$$, where the given expression extends to an infinite number of fractions, then what is the value of x?

$$2=x*(1+\frac{2}{1+\frac{2}{1+...}})$$
--> $$2= x*(1 + x)$$

$$x^{2}+ x-2 =0$$

$$(x-1)(x+2)=0$$

--> $$x_1= 1$$, $$x_2= -2$$
(x is positive)--> $$x= 1$$

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Re: If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi  [#permalink]

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04 Mar 2020, 02:41
1
So, the equation is basically=>

x = 2 / (1+x)

Put x=1, it'll satisfy so A

Bunuel wrote:
If x is a positive number and $$\frac{2}{1+\frac{2}{1+\frac{2}{1+...}}}=x$$, where the given expression extends to an infinite number of fractions, then what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

Project PS Butler

Are You Up For the Challenge: 700 Level Questions
Math Expert
Joined: 02 Sep 2009
Posts: 64939
Re: If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi  [#permalink]

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06 Mar 2020, 00:58
Bunuel wrote:
If x is a positive number and $$\frac{2}{1+\frac{2}{1+\frac{2}{1+...}}}=x$$, where the given expression extends to an infinite number of fractions, then what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. 5

Project PS Butler

Are You Up For the Challenge: 700 Level Questions

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Hope it helps.
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Re: If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi  [#permalink]

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30 May 2020, 04:43
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Re: If x is a positive number and 2/(1 +(2/(1 + (2/(1 + ...), where the gi   [#permalink] 30 May 2020, 04:43