Đáp án + Giải thích các bước giải:

$x(2x - \sqrt{4}x) + x + 5 + y(y^2 + 1) - \Bigg[y(y^2 + |-1|) + \bigg(\dfrac{5}{4} + \dfrac{120}{67} + \dfrac{397}{137}\bigg)\bigg(\dfrac{5}{7} - \dfrac{165}{231}\bigg)^2\Bigg] = -2x + (1^2 + 2^2 + 3^2 + \ldots + 9^2)[z^3 + z - z(z^2 + 1)]$

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Đặt $\textbf{A} = x(2x - \sqrt{4}x) + x + y(y^2 + 1)$

$\textbf{B} = y(y^2 + |-1|) + \bigg(\dfrac{5}{4} + \dfrac{120}{67} + \dfrac{397}{137}\bigg)\bigg(\dfrac{5}{7} - \dfrac{165}{231}\bigg)^2$

$\textbf{C} = -2x + (1^2 + 2^2 + 3^2 + \ldots + 9^2)[z^3 + z - z(z^2 + 1)]$

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Lúc này $\textbf{A} - \textbf{B} = \textbf{C}$

$\textbf{A} = x(2x - \sqrt{4}x) + x + 5 + y(y^2 + 1)$

$= x(2x - 2x) + x + 5 + y(y^2 + 1)$

$= x + 5 + y(y^2 + 1)$

$\textbf{B} = y(y^2 + |-1|) + \bigg(\dfrac{5}{4} + \dfrac{120}{67} + \dfrac{397}{137}\bigg)\bigg(\dfrac{5}{7} - \dfrac{165}{231}\bigg)^2$

$= y(y^2 + 1) + \bigg(\dfrac{5}{4} + \dfrac{120}{67} + \dfrac{397}{137}\bigg)\bigg(\dfrac{165}{231} - \dfrac{165}{231}\bigg)^2$

$= y(y^2 + 1) + 0$

$= y(y^2 + 1)$

$\textbf{C} = -2x + (1^2 + 2^2 + 3^2 + \ldots + 9^2)[z^3 + z - z(z^2 + 1)]$

$= -2x + (1^2 + 2^2 + 3^2 + \ldots + 9^2)[z^3 + z - (z^3 + z)]$

$= -2x + 0$

$= -2x$

Mà $\textbf{A} - \textbf{B} = \textbf{C}$, nên ta có:

$x + 5 + y(y^2 + 1) -y(y^2 + 1) = -2x$

$x + 5 = -2x$

$3x + 5 = 0$

$x = -\dfrac{5}{3}$

Vậy $x = -\dfrac{5}{3}$