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Tính bằng cách hợp lí nhất:
1).25 va 2/13-(15/17+15 va 2/3)
2).3 va 1/11*27/46*1 va 6/17*2 va 4/9
3).75,284*15,137*(9,5-4,75*2)+231*(7,35+2,65)
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\(3\frac{3}{11}x27\frac{27}{46}x1\frac{6}{17}x2\frac{4}{9}=\frac{34x1269x23x22}{11x46x17x9}=\frac{2x17x141x9x23x2x11}{11x23x17x9}=282\)
a) \(C=75,284\cdot15,137\cdot\left(9,5-4,75\cdot2\right)+231\left(7,25+2,75\right)\)
\(C=75,284\cdot15,137\cdot\left(9,5-9,5\right)+231\cdot10\)
\(C=75,284\cdot15,137\cdot0+2310=2310\)
b) \(D=\left(1000\cdot0,1-900\cdot0,1-90\cdot0,1\right)\left(142\cdot0,5-240\cdot0,25\right)\)
\(D=\left[0,1\left(1000-900-90\right)\right]\left(142\cdot0,5-240\cdot0,5\cdot\frac{1}{2}\right)\)
\(D=\left(0,1\cdot10\right)\left(142\cdot0,5-140\cdot0,5\right)\)
\(D=0,5\left(142-140\right)\)
\(D=\frac{1}{2}\cdot2=1\)
c) \(E=3,54+73+0,23\cdot25+3,54\cdot27+0,17\cdot25\)
\(E=3,54\left(1+27\right)+73+25\left(0,23+0,17\right)\)
\(E=3,54\cdot28+73+25\cdot0,4\)
\(E=99,12+73+10\)
\(E=99,12+1+72+10\)
\(E=100,12+72+10=182,12\)
1.
b) \(3^x+3^{x+2}=2430\)
\(\Rightarrow3^x.1+3^x.3^2=2430\)
\(\Rightarrow3^x.\left(1+3^2\right)=2430\)
\(\Rightarrow3^x.10=2430\)
\(\Rightarrow3^x=2430:10\)
\(\Rightarrow3^x=243\)
\(\Rightarrow3^x=3^5\)
\(\Rightarrow x=5\)
Vậy \(x=5.\)
c) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=15\\2x-15=\pm1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=15:2\\2x-15=1\\2x-15=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\2x=16\\2x=14\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\x=8\\x=7\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{15}{2};8;7\right\}.\)
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