Khoanh vào ô đặt trước câu trả lời đúng : b) Số thích hợp viết vào chỗ chấm để 24 m 2   =   … . c m 2

A. 240

B. 2400

C. 24000

D. 240000

3.

a. Ta có: \(n^2\left(n+1\right)+2n\left(n+1\right)=n\left(n+1\right)\left(n+2\right)\)

Vì n(n+1) là hai số nguyên liên tiếp nên \(n\left(n+1\right)⋮2\)

n(n+1)(n+2) là ba số nguyên liên tiếp

Nếu \(n\left(n+1\right)\left(n+2\right)⋮3\) mà ƯCLN(2,3)=1

Vậy \(n\left(n+1\right)\left(n+2\right)⋮\left(2\cdot3\right)=6\)

b. \(55^{n+1}-55^n=55^n+55-55^n=55^n\left(55-1\right)=54\cdot55^n⋮54\)

Vậy \(55^{n+1}-55^n⋮54\)

a. \(5x^2\left(2x-3\right)+\left(2x^2+3x+3\right)\left(3-2x\right)=6x^3-9x^2\Leftrightarrow5x^2\left(2x-3\right)-\left(2x^2+3x+3\right)\left(2x-3\right)=3x^2\left(2x-3\right)\Leftrightarrow5x^2\left(2x-3\right)-\left(2x^2+3x+3\right)\left(2x-3\right)-3x^2\left(2x-3\right)=0\Leftrightarrow\left[5x^2-\left(2x^2+3x+3\right)-3x^2\right]\left(2x-3\right)=0\Leftrightarrow\left(5x^2-2x^2-3x-3-3x^2\right)\left(2x-3\right)=0\Leftrightarrow\left(2x-3\right)\left(-3x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\-3x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\-3x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1\end{matrix}\right.\)

b. \(\left(4x^2+2x\right)\left(x^2-x\right)+\left(4x^2+6\right)\left(x-x^2\right)=0\Leftrightarrow\left(4x^2+2x\right)\left(x^2-x\right)-\left(4x^2+6\right)\left(x^2-x\right)=0\Leftrightarrow\left(x^2-x\right)\left[\left(4x^2+2x\right)-\left(4x^2+6\right)\right]=0\Leftrightarrow\left(x^2-x\right)\left(4x^2+2x-4x^2-6\right)=0\Leftrightarrow x\left(2x-6\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-6=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\2x=6\\x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=1\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}x=0\\x=3\\x=1\end{matrix}\right.\)