\(\left(1-2x\right)^2=\left(2x-5\right)\left(2x-1\right)\\ < =>1^2-2.1.2x+\left(2x\right)^2=4x^2-10x-2x+5\\ < =>1-4x+4x^2=4x^2-12x+5\\ < =>4x^2-4x^2+12x-4x=5-1\\ < =>8x=4\\ < =>x=\dfrac{1}{2}=>S=\left\{\dfrac{1}{2}\right\}\)

\(Cảm\ ơn\ bạn\ nha.\)

\(4-\left(x-3\right)=7^2-1^{10}\\ =>4-x+3=49-1\\ =>7-x=48\\ =>x=7-48\\ =>x=-41\)

\(a)\)\(64x25+35x25+25\\ =25x\left(64+35+1\right)\\ =25x100=2500\)

\(b)\)\(58x42+32x8+5x16\\ =58x42+16x2x8+5x16\\ =58x42+16x\left(2x8+5\right)\\ =58x21x2+16x21\\ =21x\left(58x2+16\right)\\ =21x132=2772\)

\(Ngày\ thứ\ hai\ bạn\ đọc\ chiếm\ số\ phần\ cuốn\ sách\ là :\)

\(1-\dfrac{2}{5}=\dfrac{3}{5}\)\((cuốn\ sách)\)

\(Cuốn\ sách\ dày: \)

\(30:\dfrac{3}{5}=50\left(trang\right)\)

\(\left(2x-6y\right)^2-\left(3xy-4\right)^2\\ =\left[\left(2x-6y\right)+\left(3xy-4\right)\right].\left[\left(2x-6y\right)-\left(3xy-4\right)\right]\\ =\left(2x-6y+3xy-4\right)\left(2x-6y-3xy+4\right)\)

\(\dfrac{\sqrt{45mn^2}}{\sqrt{20m}}\left(m,n>0\right)\\ =\sqrt{\dfrac{45mn^2}{20m}}=\sqrt{\dfrac{5m.9n^2}{5m.4}}\\ =\sqrt{\dfrac{9n^2}{4}}=\sqrt{\left(\dfrac{3n}{2}\right)^2}=\left|\dfrac{3n}{2}\right|\)

\(=\dfrac{3n}{2}\) \((Vì: n>0=>3n/2>0)\)

\(ĐK:x\ne-2\)

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

\(Để\ C\in Z\) \(=>\dfrac{4}{2x+4}\in Z=>4⋮\left(2x+4\right)=>2x+4\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

\(A=\dfrac{4x+9}{2x+1}=\dfrac{2\left(2x+1\right)+7}{2x+1}=2+\dfrac{7}{2x+1}\)

\(Để A\in Z\) \(=>\dfrac{7}{2x+1}\in Z\)

\(=>7⋮\left(2x+1\right)=>2x+1\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

\(\left(x^2+4x+4\right):\left(x+2\right)-\left(ĐK:x\ne-2\right)\\ =\dfrac{x^2+2.x.2+2^2}{x+2}=\dfrac{\left(x+2\right)^2}{x+2}=x+2\)