\(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+...+\frac{1}{17}
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cho \(\hept{\begin{cases}a,b>\frac{\sqrt{5}-1}{2}\\a+b=ab\end{cases}}\)chung minh rang:
\(\frac{1}{a^2+a-1}+\frac{1}{b^2+b-1}\ge\frac{2}{5}\)
Cho a,b,c\(\ge0\)thoa man abc=1.Chung minh rang
\(\frac{1}{2a^3+3a+2}+\frac{1}{2b^3+3b+2}+\frac{1}{2c^3+3c+2}\)\(\ge\frac{3}{7}\)
Cho x,y,z la cac so thuc duong thoa man xyz=2
Chung minh rang:\(\frac{x}{2x^2+y^2+5}+\frac{2y}{6y^2+z^2+6}+\frac{4z}{3z^2+4x^2+16}\le\frac{1}{2}\)
cho 1/a+1/b+1/c=2 va :a+b+c=abc .chung minh rang: \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=2\)
B=1.2.3...2012.(\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}\))
Chung minh rang B chai het cho 2013
giờ để đúng rồi đó anh em
Cho a,b.c la cac so duong va abc = 1
Chung minh rang \(\frac{1}{a^2+2b^2+3}+\frac{1}{b^2+2c^2+3}+\frac{1}{c^2+2a^2+3}\le\frac{1}{2}\)
chung minh
\(\frac{1}{\sqrt{3}}+\frac{1}{3\sqrt{2}}+\frac{1}{\sqrt{3}}\sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}}=\frac{\sqrt{3}}{\sqrt{2}}\)\(\frac{\sqrt{3}}{\sqrt{2}}\)
giải càng nhanh càng tốt !
p=\(\left(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}\right):\frac{\sqrt{x}-1}{2}\)
a) rut gon a
b)chung minh rang P>0 , \(x\ne1\)
tra loi nhanh giup minh nha. cam on nhiu
Cho 3 so duong thoa man\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\) . Chung minh rang \(\sqrt{x+yz}+\sqrt{y+zx}+\sqrt{z+xy}\)lon hon hoac bang\(\sqrt{xyz}+\sqrt{x}+\sqrt{y}+\sqrt{z}\)