\(\dfrac{2x^2}{3y^2}\cdot\dfrac{y^2}{x-2ax}+\dfrac{3x}{3a}=\dfrac{2x}{3\left(1-2a\right)}+\dfrac{3x}{3a}=\dfrac{2x}{3\left(1-2a\right)}+\dfrac{x}{a}.\)
Xác định a để 2 hệ phương trình sau là tương đương
a) \(\hept{\begin{cases}2x-3y=5\\4x+y=3\end{cases}}\)và \(\hept{\begin{cases}2x-3y=5\\12x+3y=a\end{cases}}\) b) \(\hept{\begin{cases}x-y=2\\3x+y=1\end{cases}}\)và \(\hept{\begin{cases}2ax-2y=1\\x+ay=2\end{cases}}\)
Cho x,y khác 0.
CMR : \(\frac{2x^2+3y^2}{2x^3+3y^3}+\frac{3x^2+2y^2}{3x^3+2y^3}\le\frac{4}{x+y}\)
Giải hpt
a)\(\left\{{}\begin{matrix}\dfrac{4}{2x-3y}+\dfrac{5}{3x+y}=-2\\\dfrac{3}{3x+y}-\dfrac{5}{2x-3y}=21\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\dfrac{7}{x-y+2}-\dfrac{5}{x+y-1}=\dfrac{9}{2}\\\dfrac{3}{x-y+2}+\dfrac{2}{x+y-1}=4\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}\dfrac{3}{2x-y}-\dfrac{6}{x+y}=-1\\\dfrac{1}{2x-y}-\dfrac{1}{x+y}=0\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\dfrac{4}{x+y-1}-\dfrac{5}{2x-y+3}=\dfrac{5}{2}\\\dfrac{3}{x+y-1}+\dfrac{1}{2x-y+3}=\dfrac{7}{5}\end{matrix}\right.\)
e)\(\left\{{}\begin{matrix}\dfrac{6}{x-2y}+\dfrac{2}{x+2y}=3\\\dfrac{3}{x-2y}+\dfrac{4}{x+2y}=-1\end{matrix}\right.\)
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 \(2x-y=1\)
\(2x^2+xy-y^2-3y=-1\)
b) Giải hệ phương trình 1/(3x) + (2x)/(3y) = (x + sqrt(y))/(2x ^ 2 + y); 2(2x + sqrt(y)) = sqrt(2x + 6) - y
tìm a và b để phương trình sau có nghiệm
\(\hept{\begin{cases}2ax+3by=4a+9b\\2b^2\left(x-1\right)+3a^2\left(y-2\right)=3a^2+2b^2\end{cases}}\)
Giải hệ: \(\hept{\begin{cases}x+\sqrt{x^2-2x+5}=3y+\sqrt{y^2+4}\\x^2-y^2-3x+3y+1=0\end{cases}}\)
gải hệ 2y^2-3y+1+ căn (y-1)=x^2 + căn x +xy và căn (2x+y) - căn (-3x+2y+4)+ 3x^2-14x-8=0
Giaỉ hệ phương trình :
\(\hept{\frac{\frac{1}{3x}+\frac{2x}{3y}=\frac{x+\sqrt{y}}{2x^2+y}\left(1\right)}{\sqrt{y+\sqrt{y}+x+2}+\sqrt{3x+1}=5\left(2\right)}}\)
1) 8y^2-25=3xy+5x
2)xy-2y-3=3x-x^2
3)x^2+2y^2-3xy_4x-3y-26=0
4)x^2+3y^2+2xy-2x-4y-3=0
5)x^3+3x=y^3
6)x^4-2x^2y+7y^2=55
7)x^2y^2-2xy=x^2+16y^2
