Tìm x, biết:

1/ \(\left(x^{2^{ }}-x+1\right)\left(x+1\right)-x^3-3x=1\)

2/ \(\left(x+3\right)\left(x-2\right)+3x=4\left(x+\dfrac{3}{4}\right)\)

3/ \(\left(x^{2^{ }}-5\right)\left(x+2\right)+5x=2x^2+17\)

Rút gọn bằng cách thay số bằng chữ.

1/ \(2\dfrac{1}{317}.\dfrac{3}{111}-\dfrac{316}{317}.\dfrac{1}{111}-\dfrac{4}{317.111}\)

2/ \(2\dfrac{1}{315}.\dfrac{3}{651}-\dfrac{1}{105}.3\dfrac{650}{651}-\dfrac{4}{315.651}+\dfrac{4}{105}\)

3/ \(999994.999999.999992-999996.999991.999998\)

4/ \(444443.444448.444441-444445.444440.444447\)

c/m rằng:

(a + b)³ = a³ + 3a²b + 3ab² + b³

x(x + 3) (x - 3) - (x - 1) (x² + x + 1) tại x = -5/2

( x - 5 ) ( 2x + 3 ) - 2x ( x - 3 ) + x + 7 tại x = 8

C/m: n^2022 + n^2023 + n^2024 chia hết cho n^2 + n + 1