c, 6x^4+7x^3-36x^2-7x+6=0
<=> 6x^3-12x^3+19x^3-38x^2-4x-3x+6=0
<=> 6x^3(x-2)+19x^2(x-2)+2x(x-2)-3(x-2)=0
<=> (x-2)(6x^3+18x^2+x^2+3x-x-3)=0
<=> (x-2)[6x^2(x+3)+x(x+3)-1(x+3)=0
<=> (x-2)(x+3)(6x^2+3x-2x-1)=0
<=> (x-2)(x+3)(2x+1)(3x-1)=0
<=> x=2 hoặc x=-3 hoặc x=-1/2 hoặc x=-1/3
Vậy..........
cmr các phân số sau tối giản\(\frac{2n+1}{2n^2+2n}\)va \(\frac{n^3+3n+1}{7n^3+18n^2-n-2}\)
\(lim\frac{n^2-2n+3-\frac{1}{2^{n-1}}}{n^2}\)
lim\(\frac{6^{n+3}-2^{3n}}{5^{n-1}-4^n.2^{n+1}}\)
CMR: với số nguyên dương \(n\ge2\) ta có \(\frac{2n+1}{3n+2}< \frac{1}{2n+2}+\frac{1}{2n+3}+...+\frac{1}{4n+2}< \frac{3n+2}{4\left(n+1\right)}\)
CMR: với mọi số nguyên dương \(n\ge2\) ta có \(\frac{2n+1}{3n+2}< \frac{1}{2n+2}+\frac{1}{2n+3}+...+\frac{1}{4n+2}< \frac{3n+2}{4\left(n+1\right)}\)
\(\sin^3\frac{x}{3}+3\sin^3\frac{x}{3^2}+...+3^{n-1}\sin^3\frac{x}{3}=\frac{1}{4}\left(3^n\sin^3\frac{x}{3^n}-\sin x\right)\)\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{2n+1}{2n+2}<\frac{1}{\sqrt{3n+4}}\left(n\ge1\right)\)\(\left(n!\right)^2\ge n^2\ge\left(n+1\right)^{n-1}cho\left(n\ge1\right)\)\(A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...........\frac{2n-1}{2n}\)\(n\in N,n\ge2\)
C/m A<\(\frac{1}{\sqrt{3n+1}}\)
Chứng minh rằng: \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{\left(2n-1\right)}{2n}\le\frac{1}{\sqrt{3n+1}}\) ( n là số nguyên dương)
1) \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}....\frac{\left(2n-1\right)}{2n}\le\frac{1}{\sqrt{3n+1}}\)( n là số nguyên dương)
