Bài 15: Chứng minh:
a/ 3.17/24 + 2.8/15 + 1.7/8 = 4.3/4 = 3.11/30
b/ 2.4/11 + 5.2/3 + 1.7/11 = 322219/33333
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\(\frac{4,5\times16-1,7}{4,5\times15+2,8}=\frac{4,5\times15+4,5-1,7}{4,5\times15+2,8}\)
\(=\frac{4,5\times1,5+2,8}{4,5\times1,5+2,8}\)
\(=1\)
\(\frac{4,5.16-1,7}{4,5.15+2,8}\)
\(=\frac{4,5.15+4,5-1,7}{4,5.15+2,8}\)
\(=\frac{4,5.1,5+2,8}{4,5.1,5+2,8}\)
\(=1\)
a: \(A=\dfrac{3^3\cdot2^3+3^3\cdot2^2+3^3\cdot1}{-13}=\dfrac{27\left(2^3+2^2+1\right)}{-13}=-27\)
b: \(B=\dfrac{2\cdot2^{12}\cdot3^6+2^{11}\cdot3^9}{2^3\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot3^8}\)
\(=\dfrac{2^{13}\cdot3^6+2^{11}\cdot3^9}{2^{10}\cdot3^7+2^{10}\cdot5\cdot3^8}\)
\(=\dfrac{2^{11}\cdot3^6\left(2^2+3^3\right)}{2^{10}\cdot3^7\left(1+5\cdot3\right)}=\dfrac{2}{3}\cdot\dfrac{4+27}{1+15}=\dfrac{2}{3}\cdot\dfrac{31}{16}=\dfrac{31}{24}\)
c: \(C=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{35}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot2^6-7\right)}=\dfrac{10-9}{5\cdot64-7}=\dfrac{1}{313}\)
\(A=1,7+\left|3,4-x\right|\)
\(C\text{ó};\left|3,4-x\right|\)lớn hơn or =0
\(\Rightarrow\)\(1,7+\left|3,4-x\right|=1,7+0\)
\(\Rightarrow1,7+\left|3,4-x\right|=1,7\)
\(\Rightarrow\left|3,4-x\right|=0\)
\(\Rightarrow x=3,4\)
\(B=\left|x+2,8\right|-3,5\)
\(C\text{ó}:\left|x+2,8\right|\)Lớn hơn or = 0
\(\Rightarrow\left|x+2,8\right|-3,5=0-3,5\)
\(\Rightarrow\left|x+2,8\right|-3,5=-3,5\)
\(\Rightarrow\left|x+2,8\right|=0\)
\(\Rightarrow x=-2,8\)
\(C=\left|4,3-x\right|+3,7\)
\(C\text{ó}:\left|4,3-x\right|\) Lớn hơn or = 0
\(\Rightarrow\left|4,3-x\right|+3,7=0+3,7\)
\(\Rightarrow\left|4,3-x\right|+3,7=3,7\)
\(\Rightarrow\left|4,3-x\right|=0\)
\(\Rightarrow x=4,3\)