CM: \(\sqrt{2}+2< 3.5\)
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1
21 tháng 10 2017
\(P=\sqrt{a+1}+\sqrt{b+1}+\sqrt{c+1}\)
\(\frac{2}{\sqrt{3}}P=\frac{2}{\sqrt{3}}.\sqrt{a+1}+\frac{2}{\sqrt{3}}.\sqrt{b+1}+\frac{2}{\sqrt{3}}.\sqrt{c+1}\)
\(\le\frac{\frac{4}{3}+a+1}{2}+\frac{\frac{4}{3}+b+1}{2}+\frac{\frac{4}{3}+c+1}{2}\)
\(=\frac{7}{2}+\frac{1}{2}=4\)
\(\Rightarrow P\le\frac{4.\sqrt{3}}{2}=2\sqrt{3}< 3,5\)
25 tháng 8 2023
\(R=\dfrac{\sqrt{\left(-\dfrac{2}{5}\cdot\dfrac{-5}{8}\right)^3\cdot5^2}}{\sqrt[3]{\dfrac{-3^3}{4^3}\cdot\dfrac{5^2}{2^6\cdot3^2}\cdot\dfrac{5^4}{3^4}}}\)
\(=\dfrac{\sqrt{\left(\dfrac{1}{4}\right)^3\cdot5^2}}{\sqrt[3]{\dfrac{-1}{3^3}\cdot\dfrac{25^3}{16^3}}}=\dfrac{5}{8}:\dfrac{-5}{3\cdot4}=\dfrac{5}{8}\cdot\dfrac{3\cdot4}{-5}=-\dfrac{3}{2}\)
3 tháng 12 2017
2A = 2/1.3+2/3.5+....+2/(2n-1).(2n+1)
= 1-1/3+1/3-1/5+.....+1/2n-1 - 1/2n+1
= 1-1/2n+1 < 1
=> A < 1/2
=> ĐPCM
k mk nha
19 tháng 10 2017
\(R=\frac{\sqrt{\left(-\frac{2}{5}\right)^5.\left(-\frac{5}{8}\right)^3.5^2}}{\sqrt[3]{\left(-\frac{3}{4}\right)^3.\left(-\frac{5}{24}\right)^2.\left(-\frac{5}{3}\right)^4}}\)
\(=\frac{\sqrt{\frac{2^5}{5^5}.\frac{5^3}{8^3}.5^2}}{-\sqrt[3]{\frac{3^3}{4^3}.\frac{5^2}{24^2}.\frac{5^4}{3^4}}}\)
\(=\frac{\sqrt{\frac{1}{16}}}{-\sqrt[3]{\frac{1}{27}.5^6.\frac{1}{2^{12}}}}=\frac{\frac{1}{4}}{-\frac{1}{3}.5^2.\frac{1}{16}}=-\frac{12}{25}\)
30 tháng 5 2022
\(R=\dfrac{\sqrt{\dfrac{-2^5\cdot\left(-5\right)^3}{5^5\cdot8^3}\cdot5^2}}{\sqrt[3]{-\dfrac{3^3}{4^3}\cdot\dfrac{5^2}{24^2}\cdot\dfrac{5^4}{3^4}}}=\dfrac{\sqrt{\dfrac{2^5\cdot5^3\cdot5^2}{5^5\cdot2^9}}}{\sqrt[3]{-\dfrac{1}{3}\cdot\dfrac{5^6}{4^3\cdot2^6\cdot3^2}}}\)
\(=\dfrac{\sqrt{\dfrac{1}{2^4}}}{\sqrt[3]{\dfrac{-1}{3^3\cdot4^3\cdot2^6}\cdot5^6}}=\dfrac{1}{2^2}:\dfrac{-5^2}{3\cdot4\cdot2^2}=\dfrac{1}{4}\cdot\dfrac{4\cdot4\cdot3}{-25}=\dfrac{-12}{25}\)
VD
1
VD
2
Ta có:
\(\sqrt{2}+2=2+\sqrt{2}=3,414\)
Mà 3,414 < 3,5, nên:
\(\sqrt{2}+2< 3.5\)
khong duppc tinh ra so ban oi