Question

Se f(X)= X^2001 x (X-1)^2001 , então f(9) - f(3) x f(4) é igual a:

a) 9
b) 0
c) 3
d) 4
e) 2

Answer 1

$f(x)=x^{2001}\cdot(x-1)^{2001}\\f(x)=[x\cdot(x-1)]^{2001}$
_______________

$f(9)-f(3)\cdot f(4)=[9\cdot(9-1)]^{2001}-[3\cdot(3-1)]^{2001}\cdot[4\cdot(4-1)]^{2001}\\f(9)-f(3)\cdot f(4)=(9\cdot8)^{2001}-(3\cdot2)^{2001}\cdot(4\cdot3)^{2001}\\f(9)-f(3)\cdot f(4)=72^{2001}-6^{2001}\cdot12^{2001}\\f(9)-f(3)\cdot f(4)=72^{2001}-(6\cdot12)^{2001}\\f(9)-f(3)\cdot f(4)=72^{2001}-72^{2001}\\f(9)-f(3)\cdot f(4)=0$

Letra B

Answer 2

Se f(X)= X^2001 x (X-1)^2001 , então f(9) - f(3) x f(4) é
f(X)= X^2001 x (X-1)^2001


f(9) = 9^2001 x (9-1)^2001
f(9) = 9^2001 x 8^2001==>(9x8)^2001 ==> 72^2001

f(3) = 3^2001 x (3-1)^2001
f(3) = 3^2001 x 2^2001 ==> (3x2)^2001 ==> 6^2001

f(4) = X^2001 x (X-1)^2001
f(4) = 4^2001 x (4-1)^2001 ==> (4x3)^2001 ==> 12^2001

f(9) - f(3) x f(4) 

72^2001 - ( 6^2001) x (12^2001

72^2001 - ( 6x12) ^2001
 
72^2001 - 72^2001
(72-72)^2001
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