1/7+1/8+1/56=
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1.
$(5^{1986}-5^{1985}):5^{1985}=5^{1985}(5-1):5^{1985}=5-1=4$
2.
\((7^{846}+7^{847}):7^{846}=7^{846}(1+7):7^{846}=1+7=8\)
3.
\((9^{2018}-3^{4036}):6^{2006}=[(3^2)^{2018}-3^{4036}]:6^{2006}\)
$=(3^{4036}-3^{4036}):6^{2006}=0:6^{2006}=0$
4.
$(7^{80}.8^{70}-56^{70}):56^{70}$
$=[7^{10}(7.8)^{70}-56^{70}]:56^{70}$
$=[7^{10}.56^{70}-56^{70}]:56^{70}$
$=56^{70}(7^{10}-1):56^{70}=7^{10}-1$
5.
$4^{4016}:(4^{4017}-4^{4016})=4^{4016}:[4^{4016}(4-1)]$
$=4^{4016}:4^{4016}:3=1:3=\frac{1}{3}$
6.
$(12^{206}.2^{207}-24^{206}):24^{206}$
$=(12^{206}.2^{206}.2-24^{206}):24^{206}$
$=[(12.2)^{206}.2-24^{206}]:24^{206}$
$=(24^{206}.2-24^{206}):24^{206}$
$=24^{206}(2-1):24^{206}=2-1=1$
7.
$(5^2-24)^{8946}+4^{30}:2^{60}=1^{8946}+(2^2)^{30}:2^{60}$
$=1+2^{60}:2^{60}=1+1=2$
8.
$(37.8^{1007}-7.2^{3021}):8^{1007}=[37.8^{1007}-7.(2^3)^{1007}]:8^{1007}$
$=[37.8^{1007}-7.8^{1007}]:8^{1007}$
$=8^{1007}(37-7):8^{1007}=37-7=30$
1 + 1 = 2
7 + 7 = 14
9 + 8 = 17
5 + 56 = 61
4 + 25 = 29
k mk nha .
\(\left(\frac{2}{11}+\frac{1}{3}\right)\cdot x=\left(\frac{1}{7}-\frac{1}{8}\right)\cdot56\)
\(\Rightarrow\left(\frac{6}{33}+\frac{11}{33}\right)\cdot x=\left(\frac{8}{56}-\frac{7}{56}\right)\cdot56\)
\(\Rightarrow\left(\frac{6+11}{33}\right)\cdot x=\left(\frac{8-7}{56}\right)\cdot56\)
\(\Rightarrow\frac{17}{33}\cdot x=\frac{1}{56}\cdot56\)
\(\Rightarrow\frac{17}{33}\cdot x=1\)
\(\Rightarrow x=1:\frac{17}{33}=\frac{33}{17}\)
Vậy x = 33/17
\(\left[\frac{2}{11}+\frac{1}{3}\right]\cdot x=\left[\frac{1}{7}-\frac{1}{8}\right]\cdot56\)
\(\Rightarrow\left[\frac{2\cdot3}{33}+\frac{1\cdot11}{33}\right]\cdot x=\left[\frac{8}{56}-\frac{7}{56}\right]\cdot56\)
\(\Rightarrow\left[\frac{6}{33}+\frac{11}{33}\right]\cdot x=\frac{1}{56}\cdot56\)
\(\Rightarrow\frac{17}{33}\cdot x=1\)
\(\Rightarrow x=1:\frac{17}{33}=1\cdot\frac{33}{17}=\frac{33}{17}\)
\(=4+\dfrac{5}{7}+6,35+5+\dfrac{1}{8}+2,41+1+\dfrac{9}{56}+3,24\)
=1+4+5+1+6,35+2,41+3,24
=11+12=23
e) \(\dfrac{\dfrac{1}{6}-\dfrac{1}{39}+\dfrac{1}{51}}{\dfrac{1}{8}-\dfrac{1}{12}+\dfrac{1}{68}}=\dfrac{\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{13}+\dfrac{1}{17}\right)}{\dfrac{1}{4}\left(\dfrac{1}{2}-\dfrac{1}{13}+\dfrac{1}{17}\right)}=\dfrac{1}{3}:\dfrac{1}{4}=\dfrac{3}{4}\)
\(\Leftrightarrow2^{3x+3}\cdot7^y=2^{6x}\cdot7^{2x}\cdot5^{x-1}\)
=>3x+3=6x và x-1=0 và 2x=y
=>-3x=-3 và x=1 và y=2x
=>x=1 và y=2
1/7+1/8+1/56
=15/56+1/56
=\(\frac{4}{14}\)
\(\frac{1}{7}+\frac{1}{8}+\frac{1}{56}\)
= \(\frac{1.8}{7.8}+\frac{1.7}{8.7}+\frac{1}{56}\)
= \(\frac{8}{56}+\frac{7}{56}+\frac{1}{56}\)
= \(\frac{16}{56}=\frac{2}{7}\)