\(ĐKXĐ:x\le1.\)

\(\sqrt{x^2-3x-7}-\sqrt{1-x}=0.\\ \Leftrightarrow\sqrt{x^2-3x-7}=\sqrt{1-x}.\\ \Leftrightarrow x^2-3x-7=1-x.\\ \Leftrightarrow x^2-3x-7-1+x=0.\\ \Leftrightarrow x^2-2x-8=0.\\ \Leftrightarrow\left(x-4\right)\left(x+2\right)=0.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\left(koTM\right).\\x=-2\left(TM\right).\end{matrix}\right.\)

\(a,\dfrac{5}{-7}=\dfrac{5.5}{-7.5}=-\dfrac{25}{35}.\\ \dfrac{3}{5}=\dfrac{3.7}{5.7}=\dfrac{21}{35}.\\ b,\dfrac{5}{16}.\\\dfrac{3}{-8}=\dfrac{-6}{16}.\\ c,\dfrac{4}{-9}=\dfrac{-20}{45}.\\ \dfrac{7}{-15}=\dfrac{-21}{45}.\\ d,\dfrac{5}{12}=\dfrac{75}{180}.\\ \dfrac{11}{18}=\dfrac{110}{180}.\\ \dfrac{7}{30}=\dfrac{42}{180}.\\ e,\dfrac{4}{-15}=\dfrac{-80}{300}.\\ \dfrac{-7}{20}=-\dfrac{105}{300}.\\ \dfrac{7}{25}=\dfrac{84}{300}.\\ f,\dfrac{7}{10}=\dfrac{42}{60}.\\ \dfrac{11}{20}=\dfrac{33}{60}.\\ \dfrac{7}{30}=\dfrac{14}{60}.\)

\(6,5+\left[0,75-\left(8,25-1,75\right)\right].\\ =6,5+0,75-6,5.\\ =0,75\)

\(\left(\dfrac{-3}{11}:\dfrac{5}{22}\right).\left(\dfrac{-15}{3}:\dfrac{26}{3}\right).\\ =\dfrac{-3}{11}.\dfrac{22}{5}.\dfrac{-15}{3}.\dfrac{3}{26}.\\ =\dfrac{-3}{11}.\dfrac{2.11}{5}.\dfrac{-15}{3}.\dfrac{3}{2.13}.\\ =\dfrac{9}{13}.\)

\(\dfrac{5}{12}.\left(\dfrac{-3}{4}\right)+\dfrac{7}{12}.\left(\dfrac{-3}{4}\right).\\ =\left(\dfrac{-3}{4}\right).\left(\dfrac{5}{12}+\dfrac{7}{12}\right).\\ =\dfrac{-3}{4}.1=-\dfrac{3}{4}.\)

\(\dfrac{1}{7}.\dfrac{-3}{8}+\dfrac{1}{7}.\dfrac{-13}{8}.\\ =\dfrac{1}{7}.\left(\dfrac{-3}{8}-\dfrac{13}{8}\right).\\ \dfrac{1}{7}.\left(-2\right).\\ =\dfrac{-2}{7}.\)

\(\dfrac{3}{5}.\dfrac{13}{46}-\dfrac{1}{10}.\dfrac{16}{23}.\\ =\dfrac{3}{5}.\dfrac{13}{2.23}-\dfrac{1}{10}.\dfrac{16}{23}.\\ =\dfrac{1}{10}.\dfrac{39}{23}-\dfrac{1}{10}.\dfrac{16}{23}.\\ =\dfrac{1}{10}.\left(\dfrac{39}{23}-\dfrac{16}{23}\right).\\ =\dfrac{1}{10}.1.\\ =\dfrac{1}{10}.\)

\(\dfrac{2}{3}-4.\left(\dfrac{1}{2}+\dfrac{3}{4}\right).\\ =\dfrac{2}{3}-2-3.\\ =\dfrac{2}{4}-5=-\dfrac{9}{2}.\)

\(\dfrac{2}{5}+\left(-\dfrac{4}{3}\right)+\left(-\dfrac{1}{2}\right).\\ =\dfrac{2}{5}-\dfrac{4}{3}-\dfrac{1}{2}.\\ =-\dfrac{43}{40}.\\ \\ \dfrac{15}{34}+\dfrac{1}{3}+\dfrac{19}{34}-\dfrac{4}{3}+\dfrac{3}{7}.\\ =\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{1}{3}-\dfrac{4}{3}\right)+\dfrac{3}{7}.\\ =1+\left(-1\right)+\dfrac{3}{7}.\\ =0+\dfrac{3}{7}=\dfrac{3}{7}.\)

\(\left(-\dfrac{5}{6}\right)-\left(-\dfrac{3}{8}+\dfrac{1}{10}\right).\\ =-\dfrac{5}{6}+\dfrac{3}{8}-\dfrac{1}{10}.\\ =-\dfrac{67}{120}.\\ \\ \dfrac{3}{5}+\left(-\dfrac{2}{7}\right)-\left(1,2\right).\\ =\dfrac{3}{5}-\dfrac{2}{7}-\dfrac{6}{5}.\\ =\left(\dfrac{3}{5}-\dfrac{6}{5}\right)-\dfrac{2}{7}.\\ =-\dfrac{3}{5}-\dfrac{2}{7}.\\ =-\dfrac{31}{35}.\)

\(x=101-10=91.\)

\(a,\dfrac{-3}{4}x+\dfrac{7}{11}=\dfrac{3}{22}.\\ \Leftrightarrow\dfrac{-3}{4}x=\dfrac{-1}{2}.\\ \Leftrightarrow x=\dfrac{2}{3}.\)

\(b,\left|1\dfrac{1}{3}-0,4x\right|-\dfrac{5}{12}=\dfrac{1}{4}.\\ \Leftrightarrow\left|\dfrac{4}{3}-\dfrac{2}{5}x\right|=\dfrac{2}{3}.\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{4}{3}-\dfrac{2}{5}x=\dfrac{2}{3}.\\\dfrac{4}{3}-\dfrac{2}{5}x=-\dfrac{2}{3}.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}.\\x=5.\end{matrix}\right.\)

Trung bình cộng 2 đáy của mảnh đất hình thang đó là:

\(\dfrac{21,5+18}{2}=19,75\left(m\right).\)

Chiều cao của mảnh đất hình thang đó là:

\(19,75+1,2=20,95\left(m\right).\)

Diện tích của mảnh đất hình thang đó là:

\(\dfrac{\left(21,5+18\right).20,95}{2}=\dfrac{33101}{80}\left(m^2\right).\)

\(a,\sqrt{x}=5.\\ \Leftrightarrow x=25.\\ b,2\sqrt{x}+x+1=0.\\ \Leftrightarrow\left(\sqrt{x}+1\right)^2=0.\\ \Leftrightarrow\sqrt{x}+1=0.\\ \Leftrightarrow\sqrt{x}=-1.\)

(vô lý).

\(c,\sqrt{x}=x.\\ \Leftrightarrow x-\sqrt{x}=0.\\ \Leftrightarrow\sqrt{x}\left(\sqrt{x}-1\right)=0.\\ \Leftrightarrow\left[{}\begin{matrix}x=0.\\x=1.\end{matrix}\right.\)

\(d,2\sqrt{x}\ge1.\\ \Leftrightarrow\sqrt{x}\ge\dfrac{1}{2}.\\ \Leftrightarrow x\ge\dfrac{1}{4}.\\ e,3+\sqrt{x}=5.\\ \Leftrightarrow\sqrt{x}=2.\\ \Leftrightarrow x=4.\)

Gọi chiều rộng hình chữ nhật ban đầu là \(x\left(m\right);x>0.\)

\(\Rightarrow\) Chiều dài hình chữ nhật ban đầu là \(2x\left(m\right).\)

\(\Rightarrow\) Diện tích hình chữ nhật ban đầu là \(2x^2\left(m^2\right).\)

Chiều rộng hình chữ nhật khi thay đổi là \(x+5\left(m\right).\)

Chiều dài hình chữ nhật khi thay đổi là \(2x+5\left(m\right).\)

Diện tích hình chữ nhật khi thay đổi là \(\left(x+5\right)\left(2x+5\right)\left(m^2\right).\)

Vì diện tích mới tăng thêm \(325m^2\) so với diện tích cũ.

\(\Rightarrow2x^2+325=\left(x+5\right)\left(2x+5\right).\)

\(\Leftrightarrow2x^2+325=2x^2+5x+10x+25.\\ \Leftrightarrow15x=300.\\ \Leftrightarrow x=12\left(TM\right).\)

\(\Rightarrow\) Chiều rộng hình chữ nhật ban đầu là \(12\left(m\right).\)

Chiều dài hình chữ nhật ban đầu là \(12.2=24\left(m\right).\)

Diện tích hình chữ nhật ban đầu là \(12.24=288\left(m^2\right).\)

Chu vi hình chữ nhật ban đầu là: \(\left(12+24\right).2=72\left(m\right).\)