\(x^2-1+\left(x+1\right)\left(x-2\right)=0\)
\(\Leftrightarrow x^2-1+x^2-2x+x-2=0\)
\(\Leftrightarrow2x^2-x-3=0\)
\(\Leftrightarrow\left(2x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1\end{matrix}\right.\)
Vậy ...
a \(\left(x-1\right)^2-\left(y+1\right)^2=0\)
\(x+3y-5=0\)
b \(xy-2x-y+2=0\)
3x+y=8
c \(\left(x+y\right)^2-4\left(x+y\right)=12\)
\(\left(x-y\right)^2-2\left(x-y\right)=3\)
d \(2x-y=1\)
\(2x^2+xy-y^2-3y=-1\)
Giải các phương trình sau:
a \(\left(x+2\right)\left(x+\text{4}\right)\left(x+6\right)\left(x+8\right)+16=0\)
b \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=0\)
c \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4=0\)
d \(\left(x^2-3x+2\right)\left(x^2+15x+56\right)+8=0\)
\(9\left(\dfrac{x-2}{x+1}\right)^3+\left(\dfrac{x+2}{x-1}\right)^2-10\left(\dfrac{x^2-4}{x^2-1}\right)=0\)
a \(\left|x-1\right|+\left|y-2\right|=2\)
\(\left|x-1\right|+y=3\)
b \(\left|x+1\right|+\left|y-1\right|=5\)
\(\left|x+1\right|-4y+4=0\)
Tìm m để các ptr sau có nghiệm kép.Tìm nghiệm kép đó
a,\(x^2-5x-2m+5=0\)
b,\(x^2-\left(2m-1\right)x+m^2-2m+3=0\)
c,\(\left(m+3\right)x^2-\left(2m+1\right)x+\left(m-1\right)=0\)
\(0=-\frac{\left(x+2\right)^2+12}{\left(x+2\right)^2}+\frac{\left(x+1\right)^2+1}{\left(x+1\right)^2}-\frac{\left(x+3\right)^2+3}{\left(x+3\right)^2}+\frac{\left(x+4\right)^2+4}{\left(x+4\right)^2}\)
Tìm m để hai phương trình sau có nghiệm chung
a \(2x^2+\left(3m-1\right)x-3=0\) và \(6x^2-\left(2m-1\right)x-1=0\)
b \(x^2-mx+2m+1=0\) và \(mx^2-\left(2m+1\right)x-1=0\)
Giải hệ \(\left\{{}\begin{matrix}\sqrt{x^2+2y+3}+2y-3=0\\2\left(2y^3+x^3\right)+3y\left(x+1\right)^2+6\left(x+1\right)+2=0\end{matrix}\right.\)
Giải hệ\(\left\{{}\begin{matrix}\sqrt{x^2+2y+3}+2y-3=0\\2\left(2y^3+x^3\right)+3y\left(x+1\right)^2+6\left(x+1\right)+2=0\end{matrix}\right.\)
Giải hệ:\(\left\{{}\begin{matrix}\sqrt{x^2+2y+3}+2y-3=0\\2\left(2y^3+x^3\right)+3y\left(x+1\right)^2+6\left(x+1\right)+2=0\end{matrix}\right.\)
