\(ĐK:x\ne2;x\ne-3\\ PT\Leftrightarrow\left(x-2\right)\left(x+3\right)+2\left(x+3\right)=10\left(x-2\right)+50\\ \Leftrightarrow x^2+x-6+2x+6=10x-20+50\\ \Leftrightarrow x^2-13x-30=0\\ \Leftrightarrow x^2-15x+2x-30=0\\ \Leftrightarrow\left(x-15\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=15\\x=-2\end{matrix}\right.\left(tm\right)\)
Giải các pt
a) \(\sqrt{2}\sin\left(2x+\dfrac{\pi}{4}\right)=3\sin x+\cos x+2\)
b) \(\dfrac{\left(2-\sqrt{3}\right)\cos x-2\sin^2\left(\dfrac{x}{2}-\dfrac{\pi}{4}\right)}{2\cos x-1}=1\)
c) \(2\sqrt{2}\cos\left(\dfrac{5\pi}{12}-x\right)\sin x=1\)
+) Giải hệ pt: \(\left\{{}\begin{matrix}4\sqrt{x^2+4y-5}=y^2-x+10\\x^3+\left(1-y\right)x^2=\left(x+4\right)y\end{matrix}\right.\)
+) Cho a,b,c>0 và a+b+c=2017
CM: \(\dfrac{2017a-a^2}{bc}+\dfrac{2017b-b^2}{ca}+\dfrac{2017c-c^2}{ab}\ge\sqrt{2}\left(\Sigma\sqrt{\dfrac{2017-a}{a}}\right)\)
giải phương tình sau:
\(\dfrac{1}{\sin x}\)+\(\dfrac{1}{\sin\left(x-\dfrac{3\pi}{2}\right)}\)= 4\(\sin\left(\dfrac{7\pi}{4}-x\right)\)Giải các bất phương trình sau:
a) \(\left(x^2+3x-4\right)\left(3-2x\right)< 0\)
\(\dfrac{x^2+3x+4}{x^2-2}\ge0\)
\(\dfrac{x\left(x^2+4x+4\right)}{x^2-1}\ge0\)
b) \(\dfrac{3x-2}{2-x}\le-x\)
c) \(\dfrac{x-3}{x+1}>\dfrac{x+4}{x+2}\)
d) \(\dfrac{x+2}{x-2}-\dfrac{x+3}{x-2}>1\)
e) \(|2x-3|>x+1\)
f) \(|2x-5|\le x+1\)
g) \(x-4-|x^2+3x-4|>0\)
h) \(\left|x^2+4x+3\right|>\left|x^2-4x-5\right|\)
Giải các bất phương trình sau
a/ (x+1).(x-1).(3x-6)>0
b/ \(\dfrac{x+3}{x-2}\le0\)
c/ \(\dfrac{\left(2x-5\right).\left(x+2\right)}{-4x+3}\ge0\)
d/ \(\dfrac{2x-5}{3x+2}< \dfrac{3x+2}{2x-5}\)
e/ \(\dfrac{2x^2+x}{1-2x}\ge1-x\)
f/ \(\dfrac{\left(2+x\right)^5.\left(x+1\right).\left(3-x\right)^{11}}{\left(2-x\right).\left(1-x\right)^{20}}\le0\)
Giải các bất phương trình sau
a/ (x+1).(x-1).(3x-6)>0
b/ \(\dfrac{x+3}{x-2}\le0\)
c/ \(\dfrac{\left(2x-5\right).\left(x+2\right)}{-4x+3}\ge0\)
d/ \(\dfrac{2x-5}{3x+2}< \dfrac{3x+2}{2x-5}\)
e/ \(\dfrac{2x^2+x}{1-2x}\ge1-x\)
f/ \(\dfrac{\left(2+x\right)^5.\left(x+1\right).\left(3-x\right)^{11}}{\left(2-x\right).\left(1-x\right)^{20}}\le0\)
giải pt đối xứng loại 2 hai ẩn sau:
\(\left\{{}\begin{matrix}2x^2=y+\dfrac{1}{y}\\2y^2=x+\dfrac{1}{x}\end{matrix}\right.\)
Giải bất phương trình sau:
a. \(\left|\dfrac{3-2\left|x\right|}{1-x}\right|\le1\)
b. \(\left|x+2\right|+\left|-2x+1\right|< x+1\)
Mọi người giúp mình với. Mình xin cảm ơn
1.tìm m để pt có nghiệm duy nhất \(\dfrac{x-m}{x+1}=\dfrac{x-2}{x-1}\)
2. giải hệ phương trình \(\left\{{}\begin{matrix}x^2+8y^2=12\\x^3+2xy^2+12y=0\end{matrix}\right.\)
