\(\dfrac{10^3+2.5^3+5^3}{55}\)
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\(\dfrac{10^3+2.5^3+5^3}{55}=\dfrac{\left(2.5\right)^3+2.5^3+5^3}{55}=\dfrac{2.5^3+2.5^3+5^3}{55}=\dfrac{5^3\left(2+2+1\right)}{55}=\dfrac{5^2.5}{11}=\dfrac{5^3}{11}=\dfrac{125}{11}\)
\(\dfrac{10^3+2.5^3+5^3}{55}=\dfrac{\left(2.5\right)^3+2.5^3+5^3}{55}\)
\(\Rightarrow\)\(\dfrac{5^3\left(2+2+2\right)}{55}\)=\(\dfrac{5^3}{11}\)=\(\dfrac{125}{11}\)
\(=\dfrac{5^3\left(2^3+2+1\right)}{55}-\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=5^2-\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=25-\dfrac{2}{3}\cdot\dfrac{6}{5}\)
=25-4/5
=24,2
\(\frac{10^3+2\times5^3+5^3}{55}\)= \(\frac{1000+2\times125+125}{55}\)= \(\frac{1000+250+125}{55}\)= \(\frac{1250+125}{55}\)= \(\frac{1375}{55}\)= 25.
Ta có:
\(\frac{10^{3^{ }}+2.5^3+5^3}{55}=\frac{5^3\left(2^3+2+1\right)}{55}=\frac{5^3.11}{55}=25\)
62 . 10 : { 780 : [ 103 - ( 2 . 53 + 35 . 14 ) ] }
= 360 : { 780 : [ 1000 - ( 250 + 490 ) ] }
= 360 : { 780 : [ 1000 - 740 ] }
= 360 : { 780 : 260 }
= 360 : 3
= 120.
10\(^3\) + 2. 5\(^3\) + \(\frac{5^3}{55}\)
= 1000 + 2. 125 + \(\frac{125}{55}\)
= 1000 + 250 + \(\frac{25}{11}\)
= 1250 + \(\frac{25}{11}\)
= 1250\(\frac{25}{11}\) =\(\frac{\text{ 89575}}{88}\)
103+2.53+53:55
= 1000+2.125+125:55
= 1000+250+25/11
= \(1252\frac{3}{11}\)
\(=\dfrac{5^3\cdot2^3+2\cdot5^3+5^3}{55}=\dfrac{5^3\left(2^3+2+1\right)}{55}=5^2=25\)