Tính nhanh biểu thức sau :
M = 2. \(\frac{1}{547}\). \(\frac{3}{211}\)- \(\frac{546}{547}\). \(\frac{1}{211}\)- \(\frac{4}{547.211}\)
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M = \(2.\frac{1}{547}.\frac{3}{211}-\frac{546}{547}.\frac{1}{211}-\frac{1}{247.211}\)
M = \(\frac{6}{547.211}-\frac{546}{547.211}-\frac{4}{547.211}\)
M = \(\frac{-544}{547.211}\)
\(M=2.\frac{1}{547}.\frac{3}{211}-\frac{546}{547}.\frac{1}{211}-\frac{4}{547.211}\)
\(M=\left(2.\frac{1}{547}.\frac{3}{211}\right)-\left(\frac{546}{547}.\frac{1}{211}\right)-\left(\frac{4}{547.211}\right)\)
\(M=\frac{6}{547.211}-\frac{546}{547.211}-\frac{4}{547.211}\)
\(M=\frac{6}{115417}-\frac{546}{115417}-\frac{4}{115417}\)
\(M=\frac{-540}{115417}-\frac{4}{115417}\)
\(M=\frac{-544}{115417}\)
=>\(B=\left(2\cdot\frac{1}{547}\cdot\frac{3}{211}\right)-\left(\frac{546}{547}\cdot\frac{1}{211}\right)-\left(\frac{4}{547\cdot211}\right)\)
=>\(B=\frac{6}{547\cdot211}-\frac{546}{547\cdot211}-\frac{4}{547\cdot211}\)
=>\(B=\frac{6}{115417}-\frac{546}{115417}-\frac{4}{115417}\)
=>\(B=\frac{-544}{115417}\)
a: \(M=\dfrac{631}{315}\cdot\dfrac{1}{651}-\dfrac{1}{105}\cdot\dfrac{2603}{651}-\dfrac{4}{315\cdot651}+\dfrac{4}{105}\)
\(=\dfrac{1}{315\cdot651}\cdot\left(631-4\right)-\dfrac{1}{105}\left(\dfrac{2603}{651}-4\right)\)
\(=\dfrac{1}{105}\cdot\dfrac{1}{1953}\cdot627+\dfrac{1}{105\cdot651}\)
\(=\dfrac{1}{105\cdot651}\left(\dfrac{1}{3}\cdot627+1\right)=\dfrac{1}{105\cdot651}\cdot210=\dfrac{2}{651}\)
b: \(N=\dfrac{1095}{547}\cdot\dfrac{3}{211}-\dfrac{546}{547\cdot211}-\dfrac{4}{547\cdot211}\)
\(=\dfrac{1}{547\cdot211}\left(1095\cdot3-546-4\right)\)
\(=\dfrac{1}{547\cdot211}\cdot2735=\dfrac{5}{211}\)
A = (x - 1) (x2 - 2x + 1) + 4x(x + 1)(x - 1) - 3(1 - x)(x2 + x + 1)
= (x - 1) (x2 - 2x + 1) + 4x(x + 1)(x - 1) + 3(x - 1)(x2 + x + 1)
= (x - 1) [x2 - 2x + 1 + 3(x2 + x + 1) + 4x(x + 1)]
= (x - 1) (x2 - 2x + 1 +3x2 + 3x + 3 + 4x2 + 4x)
= (x - 1) (8x2 + 5x + 4)
Vậy A = (x - 1) (8x2 + 5x + 4)
gọi 1/547=a, 1/211=b ta đc:
\(2a.3b-546a.b-4ab< =>6ab-546ab-4ab=-544ab=\dfrac{-544}{547.211}\)
\(2\dfrac{1}{547}.\dfrac{3}{211}-\dfrac{546}{547}.\dfrac{1}{211}-\dfrac{4}{547.211}\)
\(=\left(2+\dfrac{1}{547}\right).3.\dfrac{1}{211}-\left(1-\dfrac{1}{547}\right).\dfrac{1}{211}-4.\dfrac{1}{547}.\dfrac{1}{211}\)
Đặt \(a=\dfrac{1}{547};b=\dfrac{1}{211}\)
Thay \(a=\dfrac{1}{547};b=\dfrac{1}{211}\) vào biểu thức trên , ta được :
\(\left(2+a\right).3b-\left(1-a\right)b-4ab\)
\(=6b+3ab-b+ab-4ab\)
\(=5b\)
\(=5.\dfrac{1}{211}\)
\(=\dfrac{5}{211}\)
Vậy g/t biểu thức trên là : \(\dfrac{5}{211}\)
\(-\frac{544}{115417}\)
\(-\frac{544}{115417}\)
#Hok_tốt