The 100-function

Algebra Level 2

Let $\text{Hundred}$ be a function satisfying $\text{Hundred}(x) = 100x^{100}$ . Evaluate

$\text{Hundred}(12345654321) + \text{Hundred}(12345654321) - \text{Hundred}(2^{1/100} 12345654321) .$

1 solution

Zee Ell
Aug 16, 2016

$\text {Let } a = 12345654321 \text { and the function } 100(x)= f_{100}(x) \ .$

Now, our expression can be written as:

$f_{100}(a) +f_{100}(-a) - f_{100}(2^{ \frac {1}{100}}a) =$

$= 100 × a^{100} + 100 × (-a)^{100} - 100 × (2^{ \frac {1}{100}}a)^{100} =$

$=100a^{100} + 100a^{100} - 100 × 2a^{100} = \boxed {0}$

Very right solution:) I dont understand why every one is not attempting this much simple problem!

Anandmay Patel - 4 years, 10 months ago