Công thức tổng quát:n thuộc N
3/((10n+3)(10n+13))
=(3/10)((1/(10n+3))-(1/(10n+13)))
1/13 + 3/(13×23) + 3/(23.33) + ....+3/(1993.2003)
=(3/10)(1/3-1/13+1/13-1/23+...+1/1993-1/2003)
=(3/10)(1/3-1/2003)
=200/2003
cho x,y,z la cac so nguyen duong thoa man \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=2015\)
tinh gia tri lon nhat cua bieu thuc P=\(\dfrac{xy}{x^3+y^3}+\dfrac{yz}{y^3+z^3}+\dfrac{zx}{z^{3+x^3}}\)
(\(-2^3\)) . ( \(\dfrac{3}{4}\) - 0, 25 ): ( \(2\dfrac{1}{4}\) - \(1\dfrac{1}{6}\) )
( \(3\dfrac{1}{3}\) + 2, 5 ) : ( \(3\dfrac{1}{6}\) - \(4\dfrac{1}{5}\) ) - \(\dfrac{11}{31}\)
\(A=\left(-1,5\right)^22\dfrac{2}{3}-\dfrac{1}{6}+\left(\dfrac{4}{7}-\dfrac{2}{5}\right):1\dfrac{1}{35}\)
Giải phương trình :
a. \(\dfrac{3x+4}{x-2}-\dfrac{1}{x+2}=\dfrac{4}{x^2-4}+3\)
b. \(\dfrac{3x^2-2x+3}{2x-1}=\dfrac{3x-5}{2}\)
c. \(\sqrt{x^2-4}=x-1\)
Giải các hệ phương trình :
a) \(\left\{{}\begin{matrix}-7x+3y=-5\\5x-2y=4\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}4x-2y=6\\-2x+y=-3\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}-0,5x+0,4y=0,7\\0,3x-0,2y=0,4\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}\dfrac{3}{5}x-\dfrac{4}{3}y=\dfrac{2}{5}\\-\dfrac{2}{3}x-\dfrac{5}{9}y=\dfrac{4}{3}\end{matrix}\right.\)
cho x,y,z la 3 so thuc thoa man x+y+z=a;\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=\dfrac{1}{a}\) tinh S=(\(x^5-a^5\))(\(y^7-a^7\))(\(z^9-a^9\))
Cho \(\dfrac{x}{y}=\dfrac{y}{z}=\dfrac{z}{x}\)và x+y+z≠0
Tính A=\(\dfrac{x^{33}.y^{66}}{z^{99}}\)
giải các hệ phương tình sau :
1) \(\left\{{}\begin{matrix}x+y+\dfrac{1}{x}+\dfrac{1}{y}=5\\x^2+y^2+\dfrac{1}{x^2}+\dfrac{1}{y^2}=9\end{matrix}\right.\)
2) \(\left\{{}\begin{matrix}x\left(3x+2y\right)\left(x+1\right)=12\\x^2+2y+4x-8=0\end{matrix}\right.\)
3) \(\left\{{}\begin{matrix}x-3y=\dfrac{4y}{x}\\y-3x=\dfrac{4x}{y}\end{matrix}\right.\)
giúp mình với ạ ><
1) \(\sqrt{2-x^2}+\sqrt{2-\dfrac{1}{x^2}}=4-\left(x+\dfrac{1}{x}\right)\)
2) \(x\sqrt{x}+\sqrt{12-x}=2\sqrt{3\left(x^2+1\right)}\)
3) \(\left(x+8\sqrt{x}+4\right)\left(x-\sqrt{x}+4\right)=36x\)
