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Ta có \(A=\frac{\frac{1}{4}+\frac{1}{5}+\frac{1}{6}}{\left(\frac{1}{4}+\frac{1}{5}-\frac{1}{6}\right)-\frac{1}{4.5.6}}=\frac{\frac{\left(15+12+10\right)}{60}}{\left(\frac{15+12-10}{60}\right)-\frac{1}{120}}\)\(=\frac{\frac{37}{60}}{\frac{27}{60}-\frac{1}{120}}=\frac{37}{60}:\frac{54}{120}=\frac{37}{60}.\frac{120}{54}=\frac{37.2.60}{60.2.37}=1\)
\(\frac{\frac{1}{4}+\frac{1}{5}+\frac{1}{6}}{(\frac{1}{4}+\frac{1}{5}-\frac{1}{6})-\frac{1}{4}.\frac{1}{5}.\frac{1}{6}}\)=\(\frac{\frac{37}{60}}{\frac{17}{60}-\frac{1}{120}}\)=\(\frac{\frac{37}{60}}{\frac{33}{120}}\)=\(\frac{37}{60}:\frac{33}{120}=\frac{37}{60}.\frac{120}{33}\)=\(\frac{74}{33}\)
\(\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}-\left(-\frac{5}{6}\right)-\frac{-7}{8}+\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\)
\(=\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}+\frac{5}{6}+\frac{7}{8}+\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\)
\(=\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{2}{3}-\frac{2}{3}\right)+\left(\frac{3}{4}-\frac{3}{4}\right)+\left(\frac{4}{5}-\frac{4}{5}\right)+\left(\frac{5}{6}-\frac{5}{6}\right)+\frac{7}{8}+\frac{6}{7}\)
\(=\frac{7}{8}+\frac{6}{7}=\frac{49}{56}+\frac{48}{56}=\frac{49+48}{56}=\frac{97}{56}\)
\(\frac{1}{x^4}+\frac{1}{y^4}=\frac{x^2}{x^6}+\frac{1}{y^4}\ge\frac{\left(x+1\right)^2}{x^6+y^4}\ge\frac{4x}{x^6+y^4}\)
tương tự
\(\frac{1}{y^4}+\frac{1}{z^4}\ge\frac{4y}{y^6+z^4}\);
\(\frac{1}{z^4}+\frac{1}{x^4}\ge\frac{4z}{z^6+x^4}\);
cộng vế với vế => đpcm
Dấu "=" xảy ra <=> x=y=z=1
\(=\frac{5\left(\frac{1}{3}+\frac{1}{8}-\frac{1}{7}\right)}{-4\left(\frac{1}{3}+\frac{1}{8}-\frac{1}{7}\right)}:\frac{2\left(\frac{1}{3}-\frac{1}{12}+\frac{3}{7}\right)}{ }\)
MÃu thứ hai sao ý
Cau A dat thua so chung la ra
Cau B tach mau thanh h cua 2 thua so lien tiep
Trả lời:
Theo thứ tự tăng dần là:
1,\(\frac{-7}{9},0,\frac{-40}{-50},\frac{27}{33},\frac{-6}{-4}\)
2, \(\frac{-14}{37},\frac{-14}{33},0,\frac{17}{20},\frac{18}{19},\frac{4}{3}\)
1)\(\frac{-7}{9};0;\frac{-40}{-50};\frac{27}{33};\frac{-6}{-4}\)
2)\(\frac{-14}{37};\frac{-14}{33};0;\frac{18}{19};\frac{17}{20};\frac{4}{3};\)