\(\left(3-2x\right)\left(\dfrac{4}{7}x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}3-2x=0\\\dfrac{4}{7}x+2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=3\\\dfrac{4}{7}x=-2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)

Vậy: \(x=\dfrac{3}{2};x=-\dfrac{7}{2}\)

\(5,43\cdot78-43\cdot48+30\cdot80-30\cdot23\\ =43\cdot\left(78-48\right)+30\cdot\left(80-23\right)\\ =43\cdot30+30\cdot57\\ =30\cdot\left(43+57\right)\\ =30\cdot100\\ =3000\\ 6,64\cdot57+64\cdot43-2300\\ =64\cdot\left(57+43\right)-2300\\ =64\cdot100-2300\\ =6400-2300\\ =4100\\ 7,31\cdot15-31\cdot50+69\cdot125\\ =31\cdot\left(175-50\right)+69\cdot125\\ =31\cdot125+69\cdot125\\ =\left(31+69\right)\cdot125\\ =100\cdot125\\ =12500\\ 8,205-\left[1200-\left(4^2-2\cdot3\right)^3\right]:40\\ =205-\left[1200-\left(16-6\right)^3\right]:40\\ =205-\left[1200-1000\right]:40\\ =205-200:40\\ =205-5\\ =200\)

\(1,176+228+272+324\\ =\left(176+324\right)+\left(228+272\right)\\ =500+500\\ =1000\\ 2,526-131-326+321\\ =\left(526-326\right)+\left(-131+321\right)\\ =200+190\\ =390\\ 3,545\cdot65+15\cdot545-80\cdot445\\ =545\cdot\left(65+15\right)-80\cdot445\\ =545\cdot80-80\cdot445\\ =80\cdot\left(545-445\right)\\ =80\cdot100=8000\\ 4,31\cdot175-31\cdot50+69\cdot125\\ =31\cdot\left(175-50\right)+69\cdot125\\ =31\cdot125+69\cdot125\\ =125\cdot\left(31+69\right)\\ =125\cdot100\\ =12500\)

\(\left(x-2y\right)\left(x+2y\right)-\left(x-y\right)^2\\ =x^2-\left(2y\right)^2-\left(x^2-2xy+y^2\right)\\ =x^2-4y^2-x^2+2xy-y^2\\ =-5y^2+2xy\)

\(a,\left(x-2\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)

\(b,x^2-3x=0\\ \Rightarrow x\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)

Số cây gỗ trong khu vườn là:

\(120-80=40\) (cây)

Tỉ số % của số cây lấy gỗ và số cây ăn quả là:

\(40:80=0,5=50\%\)

Đáp số: \(50\%\)

\(36^{15}< 6^x\le216^{16}\\ \Rightarrow\left(6^2\right)^{15}< 6^x\le\left(6^3\right)^{16}\\ \Rightarrow6^{30}< 6^x\le6^{48}\\ \Rightarrow x=\left\{31;32;33;34;35;36;37;38;39;40;41;42;43;44;45;46;47;48\right\}\)

\(\dfrac{x+2}{3}=\dfrac{3x-2}{4}\\ \Rightarrow\left(x+2\right)\cdot4=\left(3x-2\right)\cdot3\\ \Rightarrow4x+8=9x-6\\ \Rightarrow9x-4x=8+6\\ \Rightarrow5x=14\\ \Rightarrow x=\dfrac{14}{5}\)

\(a,\left(x-1\right)\left(x-2\right)-\left(x-3\right)\left(x-4\right)=14\\ \Rightarrow x^2-3x+2-\left(x^2-7x+12\right)=14\\ \Rightarrow x^2-3x+2-x^2+7x-12=14\\ \Rightarrow4x-10=14\\ \Rightarrow4x=24\\ \Rightarrow x=6\\ b,6-4:\left(x-1\right)=2\\ \Rightarrow4:\left(x-1\right)=4\\ \Rightarrow x-1=4:4\\ \Rightarrow x=1+1\\ \Rightarrow x=2\)

Vì: \(4< 7\) và \(5< 90\) nên \(4^5< 7^{90}\)

Vậy: \(4^5< 7^{90}\)