Nếu \(\frac{x}{3}\)<0 thì x<0
Nếu \(\frac{x}{3}\)=0 thì x=0
Nếu 0<\(\frac{x}{3}\)<1 thì 0<x<3
Nếu \(\frac{x}{3}\)<0 thì x<0
Nếu \(\frac{x}{3}\)=0 thì x=0
Nếu 0<\(\frac{x}{3}\)<1 thì 0<x<3
Cho x, y, z là các số khác không. Chứng minh rằng:
Nếu \(x+y+z=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\) thì \(\frac{x^6+y^6+z^6}{x^3+y^3+z^3}=xyz\)
Giúp với!!
cho x>1,y>0 .Cmr: \(\frac{1}{\left(x-1\right)^3}+\frac{\left(x-1\right)^3}{y^3}+\frac{1}{y^3}\ge3\left(\frac{3-2x}{x-1}+\frac{x}{y}\right)\)
giải pt
a) \(x^2+4x-3\left|x+2\right|+4=0\)
b) \(\left(x+2\right)^2-3\left|x+2\right|-4=0\)
c) \(\left(x^2-3\right)^2-6\left|x^2-3\right|+5=0\)
d) \(\frac{x^2-4x+4}{x^2-2x+1}+\frac{\left|2x-4\right|}{x-1}=3\)
e) \(\left|\frac{2x-1}{x+2}\right|-2\left|\frac{x+2}{2x-1}\right|=1\)
f) \(x^2+\frac{1}{x^2}-10=2\left|x-\frac{1}{x}\right|\)
bài 2: giải các bpt sau:
1) (x-2)(\(9-x^2\))≤0
2) (\(x^2-x-6\))(\(x^2-3x+2\))≥0
3) \(\frac{\left(x-2\right)\left(9-x\right)}{x-1}\)≤0
4) \(\frac{x\left(x^2-3x+2\right)}{x+4}\)≥0
5) \(\frac{\left(x+2\right)}{\left(x+1\right)\left(x-2\right)}\)<0
6) \(\frac{\left(x-2\right)\left(9-x^2\right)}{x-1}\)≥0
7) \(\frac{x^2\left(x-3\right)}{3x^2+x-4}\)≥0
8) \(\frac{x^2-3x+2}{9-x}\)≥0
9) \(\frac{x^2+1}{x^2+3x-10}\)≤0
10) \(\frac{x^2-9x+14}{x^2+9x+14}\)≥0
giải hệ phương trình :
(x2+3) (y2+1)+10xy=0
và \(\frac{x}{x^2+3}+\frac{y}{y^2+1}+\frac{3}{20}\) =0
giải pt
a) \(3\sqrt{x}+\frac{3}{2\sqrt{x}}=2x+\frac{1}{2x}-7\)
b) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
c) \(\sqrt{2x^2+8x+5}+\sqrt{2x^2-4x+5}=6\sqrt{x}\)
d) \(x+1+\sqrt{x^2-4x+1}=3\sqrt{x}\)
e) \(x^2+2x\sqrt{x-\frac{1}{x}}=3x+1\)
f) \(x^2-6x+x\sqrt{\frac{x^2-6}{x}}-6=0\)
g) \(\frac{3x^2}{3+\sqrt{x}}+6+2\sqrt{x}=5x\)
h) \(\frac{x^2}{4-3\sqrt{x}}+8=3\left(x+2\sqrt{x}\right)\)
cho x,y,z>0 và xyz=1. Cmr: \(\frac{x^2}{1+y}+\frac{y^2}{1+z}+\frac{z^2}{1+x}\ge\frac{3}{2}\)
Giải phương trình
\(x^5-15x^3+45x-27=0\)
\(\frac{11}{x^2}-\frac{25}{\left(x+5\right)^2}=1\)
\(\left\{{}\begin{matrix}x^3-xy^2+2000y=0\\y^3-yx^2-500x=0\end{matrix}\right.\)
B1 Giai các phương trình sau
1 3(2x-1)-(3+x)=x-2
2 4x+3-2(x-1)=0
3\(\frac{x}{x+1}-\frac{2}{x-2}=1\)