0,75 x 4/3 + 5/13 : 1/26
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LK
0
DT
1
3 tháng 6 2023
=>1/4:(x-2/3)=2
=>(x-2/3)=1/8
=>x=1/8+2/3=3/24+16/24=19/24
3 tháng 6 2023
13/4 - 1/4 : ( x - 2/3 )= 5/4
\(\Rightarrow\) 1/4 : ( x- 2/3 ) = 13/4 - 5/4
\(\Rightarrow\) 1/4 : ( x- 2/3)= 2
\(\Rightarrow\) x - 2/3 = 1/4 :2
\(\Rightarrow\) x- 2/3 = 1/8
\(\Rightarrow\) x= 1/8 +2/3 =19/24
Vậy x = 19/24
AT
12 tháng 7 2021
\(\sqrt{13+\sqrt{48}}=\sqrt{13+\sqrt{4.12}}=\sqrt{13+2\sqrt{12}}=\sqrt{\left(\sqrt{12}+1\right)^2}\)
\(=\sqrt{12}+1=2\sqrt{3}+1\)
\(\Rightarrow\sqrt{5-\sqrt{13+\sqrt{48}}}=\sqrt{5-2\sqrt{3}-1}=\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=\sqrt{3}-1\)
\(\Rightarrow\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}=\sqrt{3+\sqrt{3}-1}=\sqrt{2+\sqrt{3}}\)
\(\Rightarrow\sqrt{\dfrac{4+2\sqrt{3}}{2}}=\sqrt{\dfrac{\left(\sqrt{3}+1\right)^2}{2}}=\dfrac{\sqrt{3}+1}{\sqrt{2}}\)
\(\Rightarrow2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}==2.\dfrac{\sqrt{3}+1}{\sqrt{2}}=\sqrt{6}+\sqrt{2}\)
2) biến đổi khúc sau như câu 1:
\(\Rightarrow\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}=\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)
AT
12 tháng 7 2021
1) Ta có: \(\sqrt{5-\sqrt{13+\sqrt{48}}}=\sqrt{5-\sqrt{13+\sqrt{4.12}}}=\sqrt{5-\sqrt{13+2\sqrt{12}}}\)
\(=\sqrt{5-\sqrt{\left(\sqrt{12}\right)^2+2.\sqrt{12}+1^2}}=\sqrt{5-\sqrt{\left(\sqrt{12}+1\right)^2}}=\sqrt{5-\left|\sqrt{4.3}+1\right|}\)
\(=\sqrt{5-\left(2\sqrt{3}+1\right)}=\sqrt{5-2\sqrt{3}-1}=\sqrt{4-2\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{3}\right)^2-2.\sqrt{3}.1+1^2}=\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)
\(\Rightarrow2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}=2\sqrt{3+\sqrt{3}-1}=2\sqrt{2+\sqrt{3}}\)
\(=2\sqrt{\dfrac{4+2\sqrt{3}}{2}}=2\sqrt{\dfrac{\left(\sqrt{3}\right)^2+2.\sqrt{3}.1+1^2}{2}}=2\sqrt{\dfrac{\left(\sqrt{3}+1\right)^2}{2}}\)
\(=2.\dfrac{\left|\sqrt{3}+1\right|}{\sqrt{2}}=\sqrt{2}\left(\sqrt{3}+1\right)=\sqrt{6}+\sqrt{2}\)
2) Ta có: \(\sqrt{5-\sqrt{13+\sqrt{48}}}=\sqrt{3}-1\) (như trên)
\(\Rightarrow\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}=\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{3}\right)^2+2.\sqrt{3}.1+1^2}=\sqrt{\left(\sqrt{3}+1\right)^2}=\left|\sqrt{3}+1\right|=\sqrt{3}+1\)
18 tháng 5 2016
Đặt A=1/1*2+1/2*3+...+1/13*14
=> A=1-1/2+1/2-1/3+...+1/13-1/14
=> A=1-1/14
=> A=13/14
O
27 tháng 4 2022
a) \(0,75+\left(\dfrac{-1}{3}\right)-\dfrac{5}{18}=\dfrac{3}{4}+\left(\dfrac{-1}{3}\right)-\dfrac{5}{18}=\dfrac{5}{12}-\dfrac{5}{18}=\dfrac{5}{36}\)
c) \(\dfrac{4}{15}\cdot\dfrac{1}{3}\cdot\dfrac{15}{20}=\dfrac{4}{15}\cdot\dfrac{1}{3}\cdot\dfrac{3}{4}=\dfrac{5}{45}\cdot\dfrac{3}{4}=\dfrac{15}{180}=\dfrac{1}{12}\)
d) \(\left(\dfrac{-1}{9}\right)\cdot\left(\dfrac{15}{22}\right):\left(\dfrac{-25}{9}\right)=\dfrac{-5}{66}:\left(\dfrac{-25}{9}\right)=\dfrac{-5}{66}\cdot\left(\dfrac{9}{-25}\right)=\dfrac{-3}{-110}=\dfrac{3}{110}\)
27 tháng 4 2022
a) \(0,75\) + \(\dfrac{-1}{3}\) - \(\dfrac{5}{18}\)= \(\dfrac{5}{12}\) - \(\dfrac{5}{18}\) = \(\dfrac{5}{36}\)
b) \(\dfrac{4}{15}\)x \(\dfrac{1}{3}\)x \(\dfrac{15}{20}\)= 4/45 x 15/20 = 1/15
c) -1/9 x 15/22 : -25/9 = -5/66 : -25/9 = 3/110
TM
1
0,75 \(\times\) \(\dfrac{4}{3}\) + \(\dfrac{5}{13}\) : \(\dfrac{1}{26}\)
= \(\dfrac{3}{4}\) \(\times\) \(\dfrac{4}{3}\) + \(\dfrac{5}{13}\) \(\times\) \(\dfrac{26}{1}\)
= 1 + 10
= 11
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