This is Insanity !!!

Algebra Level 4

If the value of the gigantic term is a a , where ( a ∈ N a\in \mathbb{N} ), then the value of a a is?

PS: Someone requested for clarification. I would like to say to them that the problem is totally legible. Open the image in a new window, then you would get what it is. Formatting it with LATEX would have been cumbersome. This is an original problem.


The answer is 5.

Satyam Bhardwaj by Satyam Bhardwaj , 24, India

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1 solution

Let f ( x ) = x 2 + 2 x 7 f(x)=\dfrac{x^2+2x}{7} , so the equation we want to solve is simply f ( f ( f ( f ( a ) ) ) ) = a ⟹ f ( a ) = a f(f(f(f(a))))=a \implies f(a)=a

a 2 + 2 a 7 = a ⟹ a 2 + 2 a = 7 a ⟹ a 2 − 5 a = 0 \dfrac{a^2+2a}{7}=a \implies a^2+2a=7a \implies a^2-5a=0

It has two solutions, a = 0 a=0 or a = 5 a=5 , but a a is natural, hence a = 5 \boxed{a=5} .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Huh at last... You got it! This problem is a really old one and no one understood it, up until now! I guess it was ahead of its time...Hahaha!

Satyam Bhardwaj - 5 years, 9 months ago

f(f(f(f(a))))=a doesn't imply f(a)=a

Wen Z - 4 years, 10 months ago

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