Tính giá trị biểu thức :
A=\(\frac{10,07x12+20,14x141-20,14x47}{1007:0,5}\)
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Giải:
Ta có:
a^2014 + b^2014 + c^2014 = a^1007b^1007 + b^1007c^1007 + c^1007a^1007
=> 2(a^2014 + b^2014 + c^2014) = 2(a^1007b^1007 + b^1007c^1007 + c^1007a^1007)
=> ( a^1007 - b^1007 )^2 + (b^1007 - c^1007)^2 + ( c^1007 - a^1007)^2 = 0
=> a - b - c = 0
Vậy A = 0
Giải:
Ta có:
a^2014 + b^2014 + c^2014 = a^1007b^1007 + b^1007c^1007 + c^1007a^1007
=> 2(a^2014 + b^2014 + c^2014) = 2(a^1007b^1007 + b^1007c^1007 + c^1007a^1007)
=> ( a^1007 - b^1007 )^2 + (b^1007 - c^1007)^2 + ( c^1007 - a^1007)^2 = 0
=> a - b - c = 0
Vậy A = 0
Đây là cách 1:
A = 2014.(2015 - 37) - 100.(-76 + 4030)
=> A = 2014. 2015 - 2014. 37 + 1007. 76 - 1007. 4030
=> A = 1007. 2. 2015 - 1007. 2. 37 + 1007. 76 - 1007. 4030
=> A = 1007. 4030 - 1007. 74 + 1007. 76 - 1007. 4030
=> A = ( 1007. 4030 - 1007. 4030 ) + ( 1007. 76 - 1007. 74)
=> A = 0 + 1007.( 76 - 74 )
=> A = 0 + 1007 . 2
=> A = 2014
Vậy A = 2014
Và đây là cách 2: ( Hai cách hơi giống nhau nên các bạn thông cảm )
A = 2014. (2015 - 37) - 1007. (-76 + 4030)
=> A = 2014. 2015 - 2014. 37 + 1007. 76 - 1007 . 4030
=> A = 2014. 2015 - 2014. 37 + 1007. 2. 38 - 1007. 2. 2015
=> A = 2014. 2015 - 2014. 37 + 2014. 38 - 2014. 2015
=> A = ( 2014. 2015 - 2014. 2015 ) + ( 2014. 38 - 2014. 37 )
=> A = 0 + 2014. ( 38 - 37 )
=> A = 0 + 2014. 1
=> A = 2014
Vậy A = 2014
a) \(\left( {\frac{7}{3} + 3,5} \right):\left( { - \frac{{25}}{6} + \frac{{22}}{7}} \right) + 0,5\)
\(\begin{array}{l} = \left( {\frac{7}{3} + \frac{7}{2}} \right):\left( { - \frac{{25}}{6} + \frac{{22}}{7}} \right) + \frac{1}{2}\\ = \frac{{35}}{6}:\frac{{ - 25.7 + 22.6}}{{6.7}} + \frac{1}{2}\\ = \frac{{35}}{6}:\frac{{ - 43}}{{7.6}} + \frac{1}{2} = \frac{{35}}{6}.\frac{{7.6}}{{ - 43}} + \frac{1}{2}\\ = \frac{{ - 245}}{{43}} + \frac{1}{2} = \frac{{ - 245.2 + 43}}{{43.2}} = \frac{{ - 447}}{{86}}\end{array}\)
b) \(\frac{{38}}{7} + \left( { - 3,25} \right) - \frac{{17}}{7} + 4,55\)
\(\begin{array}{l} = \left( {\frac{{38}}{7} - \frac{{17}}{7}} \right) + \left( {4,55 - 3,25} \right)\\ = \frac{{38 - 17}}{7} + 1,3 = \frac{{21}}{7} +1,3\\ = 3 + 1,3 = 4,3\end{array}\)
a)
\(\begin{array}{l}\left( {0,25 - \frac{5}{6}} \right).1,6 + \frac{{ - 1}}{3}\\ =(\frac{25}{100}-\frac{5}{6}).\frac{16}{10}+\frac{-1}{3}\\= \left( {\frac{1}{4} - \frac{5}{6}} \right).\frac{8}{5} + \frac{{ - 1}}{3}\\ = \left( {\frac{6}{{24}} - \frac{{20}}{{24}}} \right).\frac{8}{5} + \frac{{ - 1}}{3}\\ = \frac{{ - 14}}{{24}}.\frac{8}{5} + \frac{{ - 1}}{3}\\ = \frac{{ - 14}}{{15}} + \frac{{ - 1}}{3}\\ = \frac{{ - 14}}{{15}} + \frac{{ - 5}}{{15}}\\ = \frac{{ - 19}}{{15}}\end{array}\)
b)
\(\begin{array}{l}3 - 2.\left[ {0,5 + \left( {0,25 - \frac{1}{6}} \right)} \right]\\ = 3 - 2.\left[ {\frac{1}{2} + \left( {\frac{1}{4} - \frac{1}{6}} \right)} \right]\\ = 3 - 2.\left( {\frac{1}{2} + \frac{1}{{12}}} \right)\\ =3-2.(\frac{6}{12}+\frac{1}{12})\\= 3 - 2.\frac{7}{{12}}\\ = 3 - \frac{7}{6}\\=\frac{18}{6}-\frac{7}{6}\\ = \frac{{11}}{6}\end{array}\)
\(\Rightarrow A=\frac{\frac{1}{2}-\frac{1}{5}+\frac{1}{7}}{\frac{3}{8}-\frac{3}{5}+\frac{3}{7}}+\frac{\frac{1}{2}+\frac{1}{3}-\frac{1}{5}}{\frac{3}{4}+\frac{1}{2}+\frac{3}{10}}\)
\(\Rightarrow A=\frac{\frac{1}{2}-\frac{1}{5}+\frac{1}{7}}{3.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{7}\right)}+\frac{\frac{1}{2}+\frac{1}{3}-\frac{1}{5}}{\frac{3}{2}.\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{5}\right)}\)
\(\Rightarrow A=\frac{1}{3}+\frac{2}{3}\)
\(\Rightarrow A=1\)
a) \(log_50,5=-0,439677\)
c) \(In\left(\dfrac{3}{2}\right)=0,405465\)
\(A=\frac{10,07\times12+20,14\times141-20,14\times47}{1007\div0,5}\)
\(A=\frac{10,07\times12+10,07\times2\times141-10,07\times2\times47}{2014}\)
\(A=\frac{10,07\times\left(12+2\times141-2\times47\right)}{2014}\)
\(A=\frac{10,07\times200}{2014}\)
\(A=\frac{2014}{2014}=1\)