Let y -1-2-1-3-1-2-1-3- - -A- 2B- sqrt15-3-2C- -2D- -s q r t 15-3 - 2

The correct option is B (sqrt15 3)/2y =12+13+12+13+....... Thus y = 12+13+y y = (3+y)(6+2y+1)⇒ 2y^2 + 7y = 3 + y. On solving, y= ( 3 ±√(15))2. Since the given ...

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Quantitative Aptitude

Equations

Let y =1/2+1/...

Question

Let y = $\frac{1}{2 + \frac{1}{3 + \frac{1}{2 + \frac{1}{3 + . . . . . . .}}}}$
What is the value of y?

-2

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(-sqrt15-3)/2

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(sqrt15-3)/2

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Solution

The correct option is D (sqrt15-3)/2
y = $\frac{1}{2 + \frac{1}{3 + \frac{1}{2 + \frac{1}{3 + . . . . . . .}}}}$

Thus y = $\frac{1}{2 + \frac{1}{3 + y}}$

$⟹ y = \frac{(3 + y)}{(6 + 2 y + 1)} \Rightarrow 2 y^{2} + 7 y = 3 + y .$
On solving, $y = \frac{(- 3 \pm \sqrt{15})}{2} .$
Since the given fraction is positive, the value of y is $\frac{(\sqrt{15} - 3)}{2}$ .

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Let y =12+13+12+13+....... What is the value of y?

The correct option is D (sqrt15-3)/2y =12+13+12+13+....... Thus y = 12+13+y ⟹y=(3+y)(6+2y+1)⇒2y2+7y=3+y. On solving, y=(−3±√15)2. Since the given fraction is positive, the value of y is (√15−3)2.

Let y = $\frac{1}{2 + \frac{1}{3 + \frac{1}{2 + \frac{1}{3 + . . . . . . .}}}}$
What is the value of y?