An algebra problem by Muhammad Maulana

Algebra Level 2

Let f ( x ) + ( x + 1 ) 3 = 2 f ( x ) + 1 f(x) + (x+1)^3 = 2 f(x) +1 . Find the value of f ( 10 ) f(10) .


The answer is 1330.

Muhammad Maulana by Muhammad Maulana , 25, Indonesia

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1 solution

Zach Abueg
Feb 1, 2017

f ( x ) + ( x + 1 ) 3 = 2 f ( x ) + 1 f(x) + (x + 1)^3 = 2f(x) + 1

f ( x ) = ( x + 1 ) 3 − 1 = x 3 + 3 x 2 + 3 x + 1 − 1 f(x) = (x + 1)^3-1 = x^3 + 3x^2 + 3x + 1 - 1

f ( 10 ) = 1 0 3 + 3 ( 1 0 2 ) + 3 ( 10 ) = 1330 f(10) = 10^3 + 3(10^2) + 3(10) = 1330

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