200 Followers problem

Algebra Level 3

Which of these numbers have a larger value?

1)

200 17 200 17 200 17 200 17 \sqrt{200 -17 \sqrt{ 200 -17 \sqrt {200 -17 \sqrt{ 200 -17 \ldots}}}}

2)

200 200 200 200 \sqrt{200 \sqrt{ 200 \sqrt {200 \sqrt{ 200 \ldots}}}}

Let a a be the value of the first nested radical, and b b be the values of the second nested radical.

If a a is greater provide the answer as, ( a + b ) 2 (a+b)^{2} , if b b is greater provide the answer as ( a b ) 2 (a-b)^{2} .


The answer is 36864.

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1 solution

Sravanth C.
May 16, 2015

Let's first solve a a ,

Let, 200 17 200 17 200 17 200 17 = x \large \sqrt{200 -17 \sqrt{ 200 -17 \sqrt {200 -17 \sqrt{ 200 -17 \ldots}}}} = x\

Therefore, 200 17 x = x \large \sqrt{200 -17x} = \ x 200 17 x = x 2 200 -17x = x^{2} x 2 + 17 x 200 = 0 x^{2}+17x-200=0 x 2 + 25 x 8 x 200 = 0 x^{2}+25x-8x-200=0 x ( x + 25 ) 8 ( x + 25 ) = 0 x(x+25)-8(x+25)=0

Hence the two values of x x are x = ( 25 ) x=(-25) and x = 8 x=8 . We can ignore the negative value, hence x = 8 \boxed{x=8}


Now, let's take b b

Let, 200 200 200 200 = y \large \sqrt{200 \sqrt{ 200 \sqrt {200 \sqrt{ 200 \ldots}}}} = \ y

Therefore, 200 y = y \large \sqrt{200y} = \ y 200 y = y 2 \large 200y = \ y^{2} 200 = y \large 200 = \ y

Hence the value of y = 200 \boxed{y=200} .


Now, as b b is greater than a a the answer is ( a b ) 2 (a-b)^{2} ( 8 200 ) 2 (8-200)^{2} ( 192 ) 2 = 36864 (-192)^{2}=\boxed{\boxed{36864}}

C H E E R S ! \huge CHEERS!

Nihar Mahajan - 6 years ago

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C H E E R S ! ! ! \huge CHEERS!!!

Sravanth C. - 6 years ago

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I don't know why but my followers are increasing so rapidly that I just can't believe it.In last 4-5 days I got 74 74 followers!

Nihar Mahajan - 6 years ago

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@Nihar Mahajan :P \huge \text{:P}

@Nihar Mahajan Well, that's most probably because of information cascading. The more popular you are, the greater the rate of increase in number of followers per some unit of time. But I'm not really sure that that's the cause.

I know that YouTube uses information cascading.

vishnu c - 6 years ago

@Nihar Mahajan O M G ! ! ! \huge OMG!!!

Sravanth C. - 6 years ago

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Thank you very much!

Sravanth C. - 6 years ago

Keep Calm. I've just reached 200 followers.

@Sravanth Chebrolu

I can keep calm, but you must be excited as heck! Congratulations buddy!

vishnu c - 6 years ago

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Thank you @vishnu c , don't forget to upvote my solution! He he . . .

Sravanth C. - 6 years ago

Great solution

Sai Ram - 5 years, 10 months ago

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Thanks a lot! ¨ \huge\ddot\smile

Sravanth C. - 5 years, 10 months ago

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