f-3-x-x-2-f-x-2x-3-4x-2-3x-1-x-R-

Question Number 161391 by cortano last updated on 17/Dec/21

f^{3} (x) + x^{2} f (x) = 2 x^{3} + 4 x^{2} + 3 x + 1

\forall x \in R

Commented by Rasheed.Sindhi last updated on 17/Dec/21

f (x) i s n o t a p o l y n o m i a l .

Commented by mr W last updated on 18/Dec/21

b u t i f t h e q u e s t i o n i s j u s t a l i t t l e b i t

d i f f e r e n t, f o r e x a m p l e

f^{3} (x) + x^{2} f (x) = 2 x^{3} + 4 x^{2} + 5 x + 1

t h e n f (x) i s n o p o l y n o m i a l m o r e .

f (x) = \sqrt[3]{\sqrt{{(x^{3} + 2 x^{2} + \frac{5 x}{2} + \frac{1}{2})}^{2} + \frac{x^{6}}{27}} + (x^{3} + 2 x^{2} + \frac{5 x}{2} + \frac{1}{2})}

- \sqrt[3]{\sqrt{{(x^{3} + 2 x^{2} + \frac{5 x}{2} + \frac{1}{2})}^{2} + \frac{x^{6}}{27}} - (x^{3} + 2 x^{2} + \frac{5 x}{2} + \frac{1}{2})}

Commented by mr W last updated on 18/Dec/21

y e s, i t i s!

a s s u m e i t i s, t h e n f (x) = a x + b .

c o m p a r i n g t h e f i r s t a n d l a s t t e r m

{i t}^{'} s e a s y t o s e e : a = 1, b = 1 .

n o w c h e c k :

f (x) = x + 1

{(x + 1)}^{3} = x^{3} + 3 x^{2} + 3 x + 1

x^{2} (x + 1) = x^{3} + x^{2}

- - - - - - - - - - - - -

Σ : 2 x^{3} + 4 x^{2} + 3 x + 1 ✓

Commented by Rasheed.Sindhi last updated on 18/Dec/21

{Y o u}^{'} r e r i g h t s i r, I m i s t o o k .