1/2 - ( 1/3 + 3/4 ) < hoặc = 1/24 - ( 1/8 - 1/3 )
Trả lời giúp ạ 3**
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\(\dfrac{5}{6}\) + \(\dfrac{7}{8}\)
= \(\dfrac{5\times4}{6\times4}\) + \(\dfrac{7\times3}{8\times3}\)
= \(\dfrac{20}{24}\) + \(\dfrac{21}{24}\)
= \(\dfrac{41}{24}\)
5/6 + 7/8 = 41/24
2 + 2/3 = 8/3
7/9 - 1/7 = 40/63
1-1/11 =10/11
2x17/81 = 34/81
9/11 : 5/6 = 54/55
3: 12/25 = 25/4
Tick cho mik nhé.
Chúc bạn học tốt nha !
ta có
\(S_2=\left(1-3\right)+\left(5-7\right)+..+\left(1997-1999\right)+2001\)
ha y \(S_2=-2-2-2..+2001=-2.500+2001=1001\)
\(S_3=\left(1-2-3+4\right)+\left(5-6-7+8\right)+..+\left(1997-1998-1999+2002\right)\)
hay \(S_3=0+0+..+0=0\)
\(S_2=\left(1-3\right)+\left(5-7\right)+...+\left(1997-1999\right)+2001\)
\(=\left(-2\right)+\left(-2\right)+....+\left(-2\right)+2001=\left(-2\right).500+2001=-1000+2001=1001\)
\(S_3=\left(0+1-2-3\right)+\left(4+5-6-7\right)+...+\left(1996+1997-1998-1999\right)+2000\)
\(=-4+\left(-4\right)+...+\left(-4\right)+2000=\left(-4\right).500+2000=0\)
A=1+3^2+3^4+...+3^100
-> 3^2A=9A=3^2+3^4+3^6+....+3^102
-> 9A-A=3^102-1( chỗ này mik làm tắt vì mỏi tay)
-> 8A=3^102-1
->A=\(\frac{3^{102}-1}{8}\)
ap dung bdt am gm
\(\sqrt{1+8a^3}=\sqrt{\left(1+2a\right)\left(4a^2-4a+1\right)}\)\(\le\frac{1+2a+4a^2-2a+1}{2}=\frac{4a^2+2}{2}=2a^2+1\)
\(\Rightarrow\frac{1}{\sqrt{1+8a^3}}\ge\frac{1}{2a^2+1}\)
tuongtu ta cung co \(\frac{1}{\sqrt{1+8b^3}}\ge\frac{1}{2b^2+1};\frac{1}{\sqrt{1+8c^3}}\ge\frac{1}{2c^2+1}\)
\(\Rightarrow\)VT\(\ge\frac{1}{2a^2+1}+\frac{1}{2b^2+1}+\frac{1}{2c^2+1}\)
tiep tuc ap dung bat cauchy-schwarz dang engel ta co
\(VT\ge\frac{1}{2a^2+1}+\frac{1}{2b^2+1}+\frac{1}{2c^2+1}\ge\frac{\left(1+1+1\right)^2}{2\left(a^2+b^2+c^2\right)+3}=\frac{3^2}{6+3}=1\)(dpcm)
dau = xay ra \(\Leftrightarrow a=b=c=1\)
\(2.\left(2x-\frac{4}{3}\right)^2+\frac{1}{4}=\frac{1}{2}\)
\(\Rightarrow\left(2x-\frac{4}{3}\right)^2=\frac{1}{2}-\frac{1}{4}\)
\(\Rightarrow\left(2x-\frac{4}{3}\right)^2=\frac{1}{4}\)
\(\Rightarrow\left(2x-\frac{4}{3}\right)=\sqrt{\frac{1}{4}}\)
\(\Rightarrow\left(2x-\frac{4}{3}\right)=\frac{1}{2}\)
\(\Rightarrow2x=\frac{1}{2}+\frac{4}{3}\)
\(\Rightarrow2x=\frac{11}{6}\)
\(\Rightarrow x=\frac{11}{6}\div2\)
\(\Rightarrow x=\frac{11}{6}\times\frac{1}{2}\)
\(\Rightarrow x=\frac{11}{12}\)
\(\frac{1}{2}-\left(\frac{1}{3}+\frac{3}{4}\right)=\frac{1}{2}-\frac{13}{12}=\frac{-7}{12}\)
\(\frac{1}{24}-\left(\frac{1}{8}-\frac{1}{3}\right)=\frac{1}{24}-\frac{-5}{24}=\frac{1}{4}\)
mk tính ra rồi nhé còn lại bạn tự so sánh đi ak