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2. \(54^{49}+54^{48}=54^{48}\left(54+1\right)=54.55=54.5.11\) chia hết cho 5 và 11
3.
+)Xét x=3k => (x+12)(x+20)(x+34)=(3k+12)(3x+20)(3k+34)=3(k+4)(3k+20)(3k+34) chia hết cho 3
+)Xét x=3k+1=>(x+12)(x+20)(x+34)=(3k+13)(3k+21)(3k+35)=(3k+13)3(k+7)(3k+35) chia hết cho 3
+)Xét x=3k+2=>(x+12)(x+20)(x+34)=(3k+14)(3k+22)(3k+36)=(3k+14)(3k+22)3(k+12) chia hết cho 3
Từ 3 trường hợp trên suy ra đpcm
\(a.\)
\(\dfrac{27}{13}-\dfrac{106}{111}+-\dfrac{5}{111}=\dfrac{27}{13}-\dfrac{106}{111}-\dfrac{5}{111}=\dfrac{27}{13}-\left(\dfrac{106+6}{111}\right)=\dfrac{27}{13}-1=\dfrac{14}{13}\)
\(b.\)
\(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+1=\dfrac{23}{11}\)
\(c.\)
\(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+-\dfrac{6}{31}=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)-\left(\dfrac{25}{31}+\dfrac{6}{31}\right)=1-1=0\)
a) \(\dfrac{27}{13}-\dfrac{106}{111}+\dfrac{-5}{111}=\dfrac{27}{13}+\left(\dfrac{-106}{111}+\dfrac{-5}{111}\right)=\dfrac{27}{13}+-1=\dfrac{14}{13}\)
b) \(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+\left(\dfrac{7}{19}+\dfrac{12}{19}\right)=\dfrac{12}{11}+1=\dfrac{23}{11}\)
c)\(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+\dfrac{-6}{31}=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)+\left(\dfrac{-25}{31}+\dfrac{-6}{31}\right)=1+-1=0\)
C=2.2+4.4+6.6+...+48.48
C=2.(4-2)+4.(6-2)+6.(8-2)+...+48.(50-2)
C=2.4-2.2+4.6-4.2+6.8-6.2+...+48.50-48.2
C=(2.4+4.6+6.8+...+48.50)-(2.2+4.2+6.2+...+48.2)
Đặt D=2.4+4.6+6.8+...+48.50
6D=2.4.6+4.6.6+6.8.6+...+48.50.6
6D=2.4.6+4.6.(8-2)+6.8.(10-4)+...+48.50.(52-46)
6D=2.4.6+4.6.8-2.4.6+6.8.10-4.6.8+...+48.50.52-46.48.50
6D=48.50.52
D=20800
ĐặtE=2.2+4.2+6.2+...+48.2
E=(2+4+6+...+48).2
đến đấy rồi bạn tình tổng 2+4+6+...+48 rồi bạn tự làm tiếp nhé
nhớ tick cho mình.Thanks bạn
a: \(=\dfrac{-39+19+10}{12}=\dfrac{-10}{12}=\dfrac{-5}{6}\)
b: \(=\dfrac{2^{30}\cdot3^{16}\cdot7-2^{34}\cdot3^{15}}{2^{28}\cdot3^{21}-2^{28}\cdot3^{17}}\)
\(=\dfrac{2^{30}\cdot3^{15}\left(3\cdot7-2^4\right)}{2^{28}\cdot3^{17}\left(3^4-1\right)}=\dfrac{2^2}{3^2}\cdot\dfrac{21-16}{80}=\dfrac{4}{9}\cdot\dfrac{5}{80}\)
\(=\dfrac{20}{720}=\dfrac{1}{36}\)
a, \(\dfrac{14}{13}-\dfrac{1}{13}-\dfrac{19}{20}=1-\dfrac{19}{20}=\dfrac{1}{20}\)
b, \(-\dfrac{24}{17}+\dfrac{7}{17}+\dfrac{1}{16}=\dfrac{-17}{17}+\dfrac{1}{16}=-1+\dfrac{1}{16}=-\dfrac{15}{16}\)
b: D=(-3/31-28/31)+(-6/17-11/17)+(1/25-5/25)
=-2-4/25=-54/25
Xét: \(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\)
\(=\dfrac{3-2-1}{6}\)
\(=0\)
\(\rightarrow C=0\)
a.\(\dfrac{19\left(3-4+1\right)}{1995.1996.1997}\)=\(\dfrac{19.0}{1995.1996.1997}\)=0
\(A=\dfrac{19.3-19.4+19}{1995.1996.1997}=\dfrac{19.3-19.4+19.1}{1995.1996.1997}=\dfrac{19.0}{1995.1996.1997}=\dfrac{0}{1995.1996.1997}=0\)b) sửa đề:
\(B=\dfrac{48.48-17}{47.48+31}=\dfrac{48.\left(47+1\right)-17}{47.48+31}=\dfrac{48.47+48-17}{47.48+31}=\dfrac{47.48+31}{47.48+31}=1\)