Giải các phương trình sau:
a) \(x^2+\dfrac{2x}{x-1}=8\)
b) \(\dfrac{x^2+2x+1}{x^2+2x+2}+\dfrac{x^2+2x+2}{x^2+2x+3}=\dfrac{7}{6}\)
c) \(\dfrac{x+4}{x-1}+\dfrac{x-4}{x+1}=\dfrac{x+8}{x-2}+\dfrac{x-8}{x+2}+6\)
d) \(\left(x^2+6x+8\right)\left(x^2+8x+15\right)=24\)
e) \(\left(x^2+x-2\right)\left(x^2+9x+18\right)=28\)
f) \(3\left(-x^2+2x+3\right)^4-26x^2\left(-x^2+2x+3\right)^2-9x^4=0\)
g) \(x^4+6x^3+11x^2+6x+1=0\)
h) \(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2=0\)
i) \(\left(x+2\right)^4+\left(x+8\right)^4=272\)
Chứng minh: \(f\left(x\right)⋮g\left(x\right)\) biết: \(f\left(x\right)=x^{99}+x^{88}+x^{77}+.............+x^{11}+1\)
\(g\left(x\right)=x^9+x^8+x^7+..............+x+1\)
1. a, tính gt nhỏ nhất của biểu thức
A=\(\frac{2x^2-16x+41}{x^2-8x+22}\)
b, tính gt lớn nhất của biểu thúc
B=\(\frac{3x^2+9x+17}{3x^2+9x+7}\)
2. cho bt Q=\(\left[\left(x^4-x+\frac{x-3}{x^3+1}\right).\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right].\frac{4x^2+4x+1}{\left(x+3\right)\left(4-x\right)}\)
Chứng minh rằng: \(8x^9-9x^8+1⋮\left(x-1\right)^2\)
Bài 1 : dùng hẳng đẳng thức để khai triển và thu gọn
a) \(\left(2x^2+\frac{1}{3}\right)^3\)
b) \(\left(2x^2y-3xy\right)^3\)
c) \(\left(-3xy^4+\frac{1}{2}x^2y^2\right)^3\)
d) \(\left(-\frac{1}{3}ab^2-2a^3b\right)^3\)
e) \(\left(x+1\right)^3-\left(x-1\right)^3-6.\left(x-1\right).\left(x+1\right)\)
f) \(x.\left(x-1\right).\left(x+1\right)-\left(x+1\right).\left(x^2-x+1\right)\)
g) \(\left(x-1\right)^3-\left(x+2\right).\left(x^2-2x+4\right)+3.\left(x-4\right).\left(x+4\right)\)
h) \(3x^2.\left(x+1\right).\left(x-1\right)+\left(x^2-1\right)^3-\left(x^2-1\right).\left(x^4+x^2+1\right)\)
k) \(\left(x^4-3x^2+9\right).\left(x^2+3\right)+\left(3-x^2\right)^3-9x^2.\left(x^2-3\right)\)
l) \(\left(4x+6y\right).\left(4x^2-6xy+9y^2\right)-54y^3\)
Chứng minh rằng: \(f\left(x\right)⋮g\left(x\right)\) biết:
\(f\left(x\right)=x^{99}+x^{88}+x^{77}+..................+x^{11}+1\)
\(g\left(x\right)=x^9+x^8+x^7+..............+x+1\) với n thuộc N
Phân tích đa thức sau thành nhân tử:
a) \(\left(x^2+8x+7\right).\left(x+3\right).\left(x+5\right)+15\)
b) \(\left(4x+1\right).\left(12x-1\right).\left(3x+2\right).\left(x+1\right)-4\)
c) \(\left(x^2+2x\right)^2+9x^2+18x+20\)
bài 1 giải phương trình
\(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)
\(\frac{3}{5x-1}+\frac{3}{3-5x}=\frac{4}{\left(1-5x\right)\left(5x-3\right)}\)
\(\frac{3}{1-4x}=\frac{2}{4x+1}-\frac{8+6x}{16x^2-1}\)
\(\frac{5-x}{4x^2-8x}+\frac{7}{8x}=\frac{x-1}{2x\left(x-2\right)}+\frac{1}{8x-16}\)
\(\frac{x+1}{x^2+x+1}-\frac{x-1}{x^2-x+1}=\frac{3}{x\left(x^4+x^2+1\right)}\)
Giải phương trình
\(\left(x^2+x+1\right)^2=3\left(x^4+x^2+1\right)\)
\(x\left(x+1\right)\left(x-1\right)\left(x+2\right)=24\)
\(2x\left(8x-1\right)^2\left(4x-1\right)=9\)
\(\left(12x+7\right)^2\left(3x+2\right)\left(2x+1\right)=3\)
