Tính nhanh:
A = \(\dfrac{1}{1975}\left(\dfrac{2}{1975}-1\right)+\left(1-\dfrac{2}{1945}\right)+\dfrac{1974}{1975}.\dfrac{1945}{1946}\)
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5 tháng 9 2018 lúc 21:13
Tính M=\(\dfrac{1}{1975}\left(\dfrac{2}{1945}-1\right)-\dfrac{1}{1945}\left(1-\dfrac{2}{1975}\right)+\dfrac{1974}{1975}\times\dfrac{1946}{1945}-\dfrac{3}{1975\times1945}\)
Ta có : P = \(\dfrac{1}{1975}\left(\dfrac{2}{1945}-1\right)-\dfrac{1}{1945}\left(1-\dfrac{2}{1975}\right)+\dfrac{1974}{1975}.\dfrac{1946}{1945}\)
\(-\dfrac{3}{1975.1945}\)
= \(\dfrac{2}{1975.1945}-\dfrac{1}{1975}-\dfrac{1}{1945}+\dfrac{2}{1975.1945}+\dfrac{1974}{1975}.\dfrac{1946}{1945}\)
\(-\dfrac{3}{1975.1945}\)
= \(\dfrac{2+2+1974.1946-3-1975-1945}{1975.1945}\)
= \(\dfrac{2+2+1974.1946-3-1975-1945}{1975.1945}\)
= \(\dfrac{1973}{1975}\)
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Tính Q = \(\dfrac{1}{1275}.\left(\dfrac{x}{1945}-1\right)-\dfrac{1}{1945}.\left(1-\dfrac{x}{1975}\right)-\dfrac{1974}{1975}.\dfrac{1946}{1945}-\dfrac{3}{1975.1945}\)
Tính nhanh giá trị của các biểu thức sau:
a) A85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2
b) B1^2-2^2+3^2-4^2+5^2-6^2+...+2011^2-2012^2
c) Cdfrac{1}{1975}left(dfrac{2}{1945}-1right)-dfrac{1}{1945}left(1-dfrac{2}{1975}right)-dfrac{1974}{1975}.dfrac{1946}{1945}-dfrac{3}{1975.1945}
d) Dleft(2^9+2^7+1right)left(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1right)
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Tính nhanh giá trị của các biểu thức sau:
a) \(A=85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)
b) \(B=1^2-2^2+3^2-4^2+5^2-6^2+...+2011^2-2012^2\)
c) \(C=\dfrac{1}{1975}\left(\dfrac{2}{1945}-1\right)-\dfrac{1}{1945}\left(1-\dfrac{2}{1975}\right)-\dfrac{1974}{1975}.\dfrac{1946}{1945}-\dfrac{3}{1975.1945}\)
d) \(D=\left(2^9+2^7+1\right)\left(2^{23}-2^{21}+2^{19}-2^{17}+2^{14}-2^{10}+2^9-2^7+1\right)\)
a) \(A=85^2-45^2+75^2-35^2+65^2-25^2+55^2-15^2\)
\(A=\left(85-45\right)\left(85+45\right)+....+\left(55-15\right)\left(55+15\right)\)
\(A=40.130+40.110+40.90+40.70\)
\(A=40.\left(130+110+90+70\right)=40.400=16000\)
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b) \(B=\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+...+\left(2011-2012\right)\left(2011+2012\right)\)
\(B=-3-7-11-...-4023\)
\(B=-\left(3+7+11+...+4023\right)\)
\(B=-\dfrac{\left(3+4023\right)\left[\dfrac{\left(4023-3\right)}{4}+1\right]}{2}=2025078\)
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\(C=\dfrac{2}{1975.1945}-\dfrac{1}{1975}-\dfrac{1}{1945}+\dfrac{2}{1975.1945}-\dfrac{1974}{1975}.\dfrac{1946}{1945}-\dfrac{3}{1974.1945}\)
\(C=\dfrac{1}{1975.1945}-\dfrac{1}{1975}-\dfrac{1}{1945}-\dfrac{\left(1975-1\right)}{1975}.\dfrac{\left(1945+1\right)}{1945}\)
\(C=\dfrac{1-1945-1975-\left(1975-1\right)\left(1945+1\right)}{1975.1945}\)
\(C=\dfrac{1-1945-1975-\left(1975.1945+1975-1945-1\right)}{1975.1945}\)
\(C=\dfrac{-2.1975-1975.1945+2}{1975.1945}\)
\(C=\dfrac{-2.1974-1975.1945}{1975.1945}=-1-\dfrac{3948}{1975.1945}\)
tới đây tự bấm máy ra kết quả nha bạn
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Xem thêm câu trả lời
\(M=\frac{1}{1975}.\left(\frac{2}{1975}-1\right)-\frac{1}{1945}.\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)
nho khô nha
Tính giá trị biểu thức
\(M=\frac{1}{1975}.\left(\frac{2}{1975}-1\right)-\frac{1}{1945}.\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)
Tính giá trị của biểu thức:
\(B=\frac{1}{1975}\left(\frac{2}{1945}-1\right)-\frac{1}{1945}\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)
Giúp mình với. Ai nhanh cho Like nhé! ^^
Rút gọn biểu thức : \(B=\frac{1}{1975}\times\left(\frac{2}{1945}-1\right)-\frac{1}{1945}\times\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}\times\frac{1946}{1945}-\frac{3}{1975\times1945}\)
Tính một cách hợp lí:
\(a)\dfrac{{{x^2} - 49}}{{{x^2} + 5}}.\left( {\dfrac{{{x^2} + 5}}{{x - 7}} - \dfrac{{{x^2} + 5}}{{x + 7}}} \right)\)
\(b)\dfrac{{19{\rm{x}} + 8}}{{x + 1975}}.\dfrac{{2000 - x}}{{x + 1945}} + \dfrac{{19{\rm{x}} + 8}}{{x + 1975}}.\dfrac{{2{\rm{x}} - 25}}{{x + 1945}}\)
\(\begin{array}{l}a)\dfrac{{{x^2} - 49}}{{{x^2} + 5}}.\left( {\dfrac{{{x^2} + 5}}{{x - 7}} - \dfrac{{{x^2} + 5}}{{x + 7}}} \right)\\ = \dfrac{{\left( {x - 7} \right)\left( {x + 7} \right)}}{{{x^2} + 5}}.\dfrac{{{x^2} + 5}}{{x - 7}} - \dfrac{{\left( {x - 7} \right)\left( {x + 7} \right)}}{{{x^2} + 5}}.\dfrac{{{x^2} + 5}}{{x + 7}}\\ = x + 7 - \left( {x - 7} \right) = 14\end{array}\)
\(\begin{array}{l}b)\dfrac{{19{\rm{x}} + 8}}{{x + 1975}}.\dfrac{{2000 - x}}{{x + 1945}} + \dfrac{{19{\rm{x}} + 8}}{{x + 1975}}.\dfrac{{2{\rm{x}} - 25}}{{x + 1945}}\\ = \dfrac{{19{\rm{x}} + 8}}{{x + 1975}}.\left( {\dfrac{{2000 - x}}{{x + 1945}} + \dfrac{{2{\rm{x}} - 25}}{{x + 1945}}} \right)\\ = \dfrac{{19{\rm{x}} + 8}}{{x + 1975}}.\dfrac{{2000 - x + 2{\rm{x}} - 25}}{{x + 1945}}\\ = \dfrac{{19{\rm{x}} + 8}}{{x + 1975}}.\dfrac{{x + 1975}}{{x + 1945}} = \dfrac{{19{\rm{x}} + 8}}{{x + 1945}}\end{array}\)
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Rút gọn biểu thức
\(B=\frac{1}{1975}.\left(\frac{2}{1945}-1\right)-\frac{1}{1945}.\left(1-\frac{2}{1975}\right)-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)
=\(\frac{1}{1975}.\frac{2}{1945}-\frac{1}{1975}-\frac{1}{1975}-\frac{1}{1975}.\frac{2}{1975}-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)
=\(\frac{1}{1975}.\left(\frac{2}{1945}-1-1-\frac{2}{1975}\right)-\frac{1974.1946}{1975.1945}-\frac{3}{1975.1945}\)
=\(\frac{1}{1975}.\left(\frac{2}{1945}-\frac{2}{1975}-2\right)-\frac{1974.1946-3}{1975.1945}\)
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