Đáp án:
$a)
x=\dfrac{13}{25}\\
b)
x=\pm \dfrac{\sqrt{66}}{10}\\
c)
x=\dfrac{-20}{13}$
Giải thích các bước giải:
$a)
(4x-1)^2-(3x-2)(3x+2)=(7x-1)(x+2)+(2x+1)^2-(4x^2+7)\\
\Leftrightarrow 16x^2-8x+1-(9x^2-4)=7x^2+14x-x-2+4x^2+4x+1-4x^2-7\\
\Leftrightarrow 16x^2-8x+1-9x^2+4=7x^2+14x-x-2+4x^2+4x+1-4x^2-7\\
\Leftrightarrow 7x^2-8x+5=7x^2+17x-8\\
\Leftrightarrow 17x+8x=5+8\\
\Leftrightarrow 25x=13\\
\Leftrightarrow x=\dfrac{13}{25}\\
b)
(2x+3)^2+(5x-4)(5x+4)=(x+5)^2-(3x-1)(7x+2)-(x^2-x+1)\\
\Leftrightarrow 4x^2+12x+9+25x^2-16=x^2+10x+25-(21x^2+6x-7x-2)-x^2+x-1\\
\Leftrightarrow 29x^2+12x-7=12x+26-21x^2\\
\Leftrightarrow 29x^2+21x^2=26+7\\
\Leftrightarrow 50x^2=33\\
\Leftrightarrow x^2=\dfrac{33}{50}\\
\Leftrightarrow x=\pm \dfrac{\sqrt{66}}{10}\\
c)
(1-3x)^2-(x-2)(9x+1)=(3x-4)(3x+4)-9(x+3)^2\\
\Leftrightarrow 1-6x+9x^2-(9x^2+x-18x-2)=9x^2-16-9(x^2+6x+9)\\
\Leftrightarrow 1-6x+9x^2-9x^2-x+18x+2=9x^2-16-9x^2-54x-81\\
\Leftrightarrow 3+11x=-54x-97\\
\Leftrightarrow 54x+11x=-3-97\\
\Leftrightarrow 65x=-100\\
\Leftrightarrow x=\dfrac{-100}{65}=\frac{-20}{13}$
