Question

Problema din poza va rog frumos dau coronița ​

Answer 1

Explicație pas cu pas:

rezolvarea in fotografie

Answer 2

Explicație pas cu pas:

a)

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

b)

$E(x) = \bigg(\dfrac{x}{x + 1} - \dfrac{x^{2} + 1}{1 + 2x + x^{2}}\bigg) : \dfrac{3x - 3 }{{x}^{3} + 2 {x}^{2} + x} =$

$= \bigg(\dfrac{x}{x + 1} - \dfrac{x^{2} + 1}{ {(x + 1)}^{2} }\bigg) : \dfrac{3(x - 1) }{x {(x + 1)}^{2} }$

$= \dfrac{x(x + 1) - x^{2} - 1}{ {(x + 1)}^{2} } \cdot \dfrac{x {(x + 1)}^{2}}{3(x - 1)}$

$= \dfrac{x - 1}{1} \cdot \dfrac{x}{3(x - 1)} = \dfrac{x}{3}$

$m_{a} = \dfrac{a + b}{2} = \dfrac{\dfrac{2 + \sqrt{3}}{3} + \dfrac{4 - \sqrt{3}}{3}}{2} = \\ = \dfrac{2 + \sqrt{3} + 4 - \sqrt{3}}{6} = \dfrac{6}{6} = \bf 1 \in \mathbb{N}$

$q.e.d.$