`1)25x²-9=0`
`⇔(5x)²-3²=0`
`⇔(5x+3)(5x-3)=0`
`⇔`\(\left[ \begin{array}{l}5x+3=0\\5x-3=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}5x=-3\\5x=3\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\dfrac{-3}{5}\\x=\dfrac{3}{5}\end{array} \right.\)
Vậy `x=(-3)/5` hoặc `x=3/5`
`2)(x+4)²-(x+1)(x-1)=16`
`⇔x²+8x+16-(x²-1)=16`
`⇔x²+8x+16-x²+1=16`
`⇔8x+17=16`
`⇔8x=16-17`
`⇔8x=-1`
`⇔x=-1/8`
Vậy `x=-1/8`
`3)(2x-1)²+(x+3)²-5(x+7)(x-7)=0`
`⇔4x²-4x+1+x²+6x+9-5(x²-49)=0`
`⇔4x²-4x+1+x²+6x+9-5x²+245=0`
`⇔2x+255=0`
`⇔2x=-255`
`⇔x=-255/2`
Vậy `x=-255/2`
`4)16x²-(4x-5)²=15`
`⇔16x²-(16x²-40x+25)=15`
`⇔16x²-16x²+40x-25=15`
`⇔40x-25=15`
`⇔40x=15+25`
`⇔40x=40`
`⇔x=1`
Vậy `x=1`
`5)(2x+3)²-4(x-1)(x+1)=49`
`⇔4x²+12x+9-4(x²-1)=49`
`⇔4x²+12x+9-4x²+4=49`
`⇔12x+13=49`
`⇔12x=49-13`
`⇔12x=36`
`⇔x=3`
Vậy `x=3`
`6)(2x+1)(1-2x)+(1-2x)²=18`
`⇔2x-4x²+1-2x+1-4x+4x²=18`
`⇔-4x+2=18`
`⇔-4x=18-2`
`⇔-4x=16`
`⇔x=-4`
Vậy `x=-4`
`7)(x-5)²-x(x-4)=9`
`⇔x²-10x+25-x²+4x=9`
`⇔-6x+25=9`
`⇔-6x=9-25`
`⇔-6x=-16`
`⇔x=16/6`
`⇔x=8/3`
Vậy `x=8/3`
`8)(4x-1)²-(2x+3)²+5(x+2)²+(x-2)(2+x)=500`
`⇔16x²-8x+1-(4x²+12x+9)+5(x²+4x+4)+x²-4=500`
`⇔16x²-8x+1-4x²-12x-9+5x²+20x+20+x²-4=500`
`⇔18x²+8=500`
`⇔18x²=500-8`
`⇔18x²=492`
`⇔x²=492/18`
`⇔x²=82/3`
`⇔`\(\left[ \begin{array}{l}x=\sqrt[]{\dfrac{82}{3}}\\x=-\sqrt[]{\dfrac{82}{3}}\end{array} \right.\)
Vậy `x=`$\sqrt[]{\dfrac{82}{3}}$ hoặc `x=`$-\sqrt[]{\dfrac{82}{3}}$
