GATE CSE 2014 Set 2 | Question: GA-5

Question

The value of $\sqrt{12+\sqrt{12+\sqrt{12+\dots}}} $is

• A. $3.464$
• B. $3.932$
• C. $4.000$
• D. $4.444$

Answer 1

$x = \sqrt{12 + x}$

$\implies x^2 = 12 + x$

$\implies x^2 - x - 12 = 0$

$\implies (x-4) (x+3) = 0$

$\implies x = 4 \text{ or } x = -3$

Correct Answer: $C$

Comments

X = 4 is taken because sum of positive terms can not be negative.

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As a matter of humor maybe, in just several seconds you can also use GATE calculator for such question.

Just keep calculating till 2-3 times and you'll notice that the pattern is diverging toward one of the answers.

Cheers!

Answer 2

there is a really interesting math trick behind it.

If you see a question like this take out the number inside it (in this case is 12)

Take consecutive numbers such as:

$n(n+1)=12$

Always remember that the answer is $n+1$

solve it you get $n=3$ and $n+1=4$

so 4 is the answer.

 

Assume that there is $"-"$ instead of positive then answer would be $n$.

[If we solve by equation then it would be $x^{2}+x-12=0$ giving $x = 3$

 

 

Comments

Thanks Sir :)