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demonstrati ca E(x)=((x^(2 )+2x+2)(x^2+2x)+1)/(x+1) este cub perfect

Răspuns :

Ardnaxela1
[tex]E(x)= \frac{(x^2+2x+2)(x^2+2x)+1}{x+1} \\\\ E(x)= \frac{x^4+2x^3+2x^3+4x^2+2x^2+4x+1}{x+1}\\\\ E(x)= \frac{x^4+4x^3+6x^2+4x+1}{x+1}\\\\ E(x) = \frac{(x+1)^4}{x+1}\\\\ E(x)=(x+1)^3=\ \textgreater \ este~cub~perfect. [/tex]

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