Tìm x biết
1) (2x - 1)'2 - (4x'2- 1) =0
2) (x + 2)'2 -x(x - 3) =2
3) (x - 5)'2 - x(x + 2) =5
4) (x - 1)'2 + x(4 - x) =11
5) (x - 3)(x + 3) =(x - 5)'2
6) (2x + 1)'2 - 4x(x - 1) =17
7) (3x + 1)'2 - 9x(x - 2) =25
8) (3x - 2)(2x + 2) - 9(x - 1)x =0
9) (x + 2)'2 - (x - 2)(x + 2) =0
10) (x + 2)'2 - (x - 3)(x + 3) =-3
\(1)\Leftrightarrow\left(2x-1\right)^2-\left(4x^2-1\right)=0\\ \Leftrightarrow\left(2x-1\right)^2-\left(2x-1\right)\left(2x+1\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(2x-1-2x-1\right)=0\\ \Leftrightarrow-2\left(2x-1\right)=0\\ \Leftrightarrow2x-1=0\\ \Leftrightarrow2x=1\\ \Leftrightarrow x=\dfrac{1}{2}\\ 2)\left(x+2\right)^2-x\left(x-3\right)=2\\ \Leftrightarrow x^2+4x+4-x^2+3x=2\\ \Leftrightarrow7x+4=2\\ \Leftrightarrow7x=2-4=-2\\ \Leftrightarrow x=\dfrac{-2}{7}\\ 3)\left(x-5\right)^2-x\left(x+2\right)=5\\ \Leftrightarrow x^2-10x+25-x^2-2x=5\\ \Leftrightarrow-12x+25=5\\ \Leftrightarrow12x=25-5=20\\ \Leftrightarrow x=\dfrac{20}{12}=\dfrac{5}{3}\\ 4)\left(x-1\right)^2+x\left(4-x\right)=11\\ \Leftrightarrow x^2-2x+1+4x-x^2=11\\ \Leftrightarrow2x+1=11\\ \Leftrightarrow2x=11-1=10\\ \Leftrightarrow x=\dfrac{10}{2}=5\\ 5)\left(x-3\right)\left(x+3\right)=\left(x-5\right)^2\\ \Leftrightarrow x^2-9=x^2-10x+25\\ \Leftrightarrow-10x+25=-9\\ \Leftrightarrow10x=25+9=34\\ \Leftrightarrow x=\dfrac{34}{10}=\dfrac{17}{5}\)
\(6)\left(2x+1\right)^2-4x\left(x-1\right)=17\\ \Leftrightarrow4x^2+4x+1-4x^2+4x=17\\ \Leftrightarrow8x+1=17\\ \Leftrightarrow8x=17-1=16\\ \Leftrightarrow x=\dfrac{16}{8}=2\\ 7)\left(3x+1\right)^2-9x\left(x-2\right)=25\\ \Leftrightarrow9x^2+6x+1-9x^2+18x=25\\ \Leftrightarrow24x+1=25\\ \Leftrightarrow24x=25-1=24\\ \Leftrightarrow x=1\\ 8)\left(3x-2\right)\left(3x+2\right)-9\left(x-1\right)x=0\\ \Leftrightarrow9x^2-4-9x\left(x-1\right)=0\\ \Leftrightarrow9x^2-4-9x^2+9x=0\\ \Leftrightarrow9x-4=0\\ \Leftrightarrow9x=4\\ \Leftrightarrow x=\dfrac{4}{9}\\ 9)\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x+2-x+2\right)=0\\ \Leftrightarrow4\left(x+2\right)=0\\ \Leftrightarrow x+2=0\\ \Leftrightarrow x=-2\\ 10)\left(x+2\right)^2-\left(x-3\right)\left(x+3\right)=-3\\ \Leftrightarrow x^2+4x+4-x^2+9=-3\\ \Leftrightarrow4x+13=-3\\ \Leftrightarrow4x=-3-13=-16\\ \Leftrightarrow x=-\dfrac{16}{4}=-4\)
