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

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

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New post 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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New post 04 Mar 2020, 01:51
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1
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\(\frac{2}{1+x} = x\)

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


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

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New post 04 Mar 2020, 01:54
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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?

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

\(x^{2}+ x-2 =0\)

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

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

The answer is A.
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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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New post 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


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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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New post 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


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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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New post 30 May 2020, 04:43
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Answer A
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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

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

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