Tính
a)\((\dfrac{3}{4}-81).(\dfrac{3^2}{5}-81).(\dfrac{3^3}{6}-81)...(\dfrac{3^{2000}}{2003}-81)\)
b)\(\dfrac{69}{157}-(2+(3+(4+5^{-1})^{-1})^{-1}\)
Những câu hỏi liên quan
Tính:
\(\left(\dfrac{3}{4}-81\right).\left(\dfrac{3^2}{5}-81\right).\left(\dfrac{3^3}{6}-81\right).....\left(\dfrac{3^{2000}}{2003}-81\right)\)
Đặt \(A=\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\left(\dfrac{3^3}{6}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(\dfrac{3^6}{9}-81\right)\cdot\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(81-81\right)\cdot\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)
=0
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1) Cho đa thức \(f\left(x\right)=x^{14}-14.x^{13}+14.x^{12}-...+13.x^2-14.x+14\) Tính f(13)
2) Tính : \(\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\left(\dfrac{3^3}{6}-81\right)...\left(\dfrac{3^{2000}}{2003}-81\right)\)
Bài 2:
x=13 nên x+1=14
\(f\left(x\right)=x^{14}-x^{13}\left(x+1\right)+x^{12}\left(x+1\right)-...+x^2\left(x+1\right)-x\left(x+1\right)+14\)
\(=x^{14}-x^{14}-x^{13}+x^{13}-...+x^3+x^2-x^2-x+14\)
=14-x=1
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x=13 nên x+1=14
f(x)=x14−x13(x+1)+x12(x+1)−...+x2(x+1)−x(x+1)+14f(x)=x14−x13(x+1)+x12(x+1)−...+x2(x+1)−x(x+1)+14
=x14−x14−x13+x13−...+x3+x2−x2−x+14=x14−x14−x13+x13−...+x3+x2−x2−x+14
=14-x=1
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Tính \(\left(\dfrac{3}{4}-81\right)\times\left(\dfrac{3^2}{5}-81\right)\times\left(\dfrac{3^3}{6}-81\right)\times....\times\left(\dfrac{3^{2000}}{2003}-81\right)\)
Câu 1:
a, Tính M 3dfrac{1}{417}cdotdfrac{1}{762}-dfrac{1}{139}cdot4dfrac{761}{762}-dfrac{4}{417cdot762}+dfrac{5}{139}
b, Tính left(dfrac{3}{4}-81right)left(dfrac{3^2}{5}-81right)left(dfrac{3^3}{6}-81right)...left(dfrac{3^{2000}}{2003}-81right)
Câu 2: Cho left(a+3right)left(b-4right)-left(a-3right)left(b+4right)0 . Chứng minh dfrac{a}{3}dfrac{b}{4}.
Đọc tiếp
Câu 1:
a, Tính M =\(3\dfrac{1}{417}\cdot\dfrac{1}{762}-\dfrac{1}{139}\cdot4\dfrac{761}{762}-\dfrac{4}{417\cdot762}+\dfrac{5}{139}\)
b, Tính \(\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\left(\dfrac{3^3}{6}-81\right)...\left(\dfrac{3^{2000}}{2003}-81\right)\)
Câu 2: Cho \(\left(a+3\right)\left(b-4\right)-\left(a-3\right)\left(b+4\right)=0\) . Chứng minh \(\dfrac{a}{3}=\dfrac{b}{4}\).
Câu 2
(a+3)(b-4)-(a-3)(b+4)=0
=>ab-4a+3b-12-ab-4a+3b+12=0
=>-8a=-6b
=>a/b=3/4
=>a/3=b/4
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Tính
a) \(2\sqrt[3]{24}-5\sqrt[3]{81}+4\sqrt[3]{192}\)
b) \(\dfrac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}.\sqrt[3]{4}\)
c) \(\dfrac{\sqrt[3]{4}+\sqrt[3]{2}}{3}-\dfrac{1}{\sqrt[3]{2}+1}\)
b: Ta có: \(\dfrac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}\cdot\sqrt[3]{4}\)
\(=\sqrt[3]{\dfrac{135}{5}}-\sqrt[3]{54\cdot4}\)
=3-6
=-3
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4 tháng 5 2022 lúc 20:30
Câu 1: Thực hiện phép tính
a, \(40\dfrac{1}{4}:\dfrac{5}{7}-25\dfrac{1}{4}:\dfrac{5}{7}-\dfrac{1}{2021}\)
b, \(\left|\dfrac{-5}{9}\right|.\sqrt{81}-2021^0.\dfrac{16}{25}\)
Câu 2: Tìm x
\(3\left(x-\dfrac{1}{3}\right)-7\left(x+\dfrac{3}{7}\right)=-2x+\dfrac{1}{3}\)
1:
a: =7/5(40+1/4-25-1/4)-1/2021
=21-1/2021=42440/2021
b: =5/9*9-1*16/25=5-16/25=109/25
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1 tháng 2 2023 lúc 21:21
Giải các phương trình sau1)dfrac{x+1}{85}+dfrac{x+3}{83}dfrac{x+5}{81}+dfrac{x+7}{79}2)dfrac{x-1}{2015}-dfrac{x+3}{2011}dfrac{x+7}{2007}-dfrac{x+11}{2003}3)dfrac{x+4}{4}-dfrac{x-3}{6}dfrac{x}{3}4)x-dfrac{x+1}{3}dfrac{2x+1}{5}5) dfrac{2x-7}{5}+dfrac{x+11}{2}-4giúp em vs ạ, em đang cần gấpem c.ơn trước ạ
Đọc tiếp
Giải các phương trình sau
1)\(\dfrac{x+1}{85}+\dfrac{x+3}{83}=\dfrac{x+5}{81}+\dfrac{x+7}{79}\)
2)\(\dfrac{x-1}{2015}-\dfrac{x+3}{2011}=\dfrac{x+7}{2007}-\dfrac{x+11}{2003}\)
3)\(\dfrac{x+4}{4}-\dfrac{x-3}{6}=\dfrac{x}{3}\)
4)\(x-\dfrac{x+1}{3}=\dfrac{2x+1}{5}\)
5) \(\dfrac{2x-7}{5}+\dfrac{x+11}{2}=-4\)
giúp em vs ạ, em đang cần gấp
em c.ơn trước ạ
1: \(\Leftrightarrow\left(\dfrac{x+1}{85}+1\right)+\left(\dfrac{x+3}{83}+1\right)=\left(\dfrac{x+5}{81}+1\right)+\left(\dfrac{x+7}{79}+1\right)\)
=>x+86=0
=>x=-86
2: \(\Leftrightarrow\left(\dfrac{x-1}{2015}+1\right)-\left(\dfrac{x+3}{2011}+1\right)=\left(\dfrac{x+7}{2007}+1\right)-\left(\dfrac{x+11}{2003}+1\right)\)
=>x+2014=0
=>x=-2014
3: \(\Leftrightarrow3\left(x+4\right)-2\left(x-3\right)=4x\)
=>4x=3x+12-2x+6
=>4x=x+18
=>3x=18
=>x=6
4: \(\Leftrightarrow15x-5\left(x+1\right)=3\left(2x+1\right)\)
=>15x-5x-5=6x+3
=>10x-5=6x+3
=>4x=8
=>x=2
5: \(\Leftrightarrow2\left(2x-7\right)+5\left(x+11\right)=-40\)
=>4x-14+5x+55=-40
=>9x+41=-40
=>x=-9
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1 tính
a. \((\left|-5\right|7^4+3^2.2\dfrac{2}{5}):(7^5.125.7^3.50)\)
b. \((\dfrac{3^2}{9}.\dfrac{3^3}{81})^{12}:(\dfrac{3^6}{81^2})^{10}\)
c. \([(\dfrac{1}{2})^2.(\dfrac{1}{3})^4.\dfrac{2}{7}]:\left(\dfrac{1}{3}\right)^{-2}.\dfrac{-2^2}{7}\)
b. \(\left(\dfrac{3^2}{9}.\dfrac{3^3}{81}\right)^{12}:\left(\dfrac{3^6}{81^2}\right)^{10}\)
\(=\left(1.\dfrac{1}{3}\right)^{12}:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left(\dfrac{1}{3}\right)^{12}:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left[\left(\dfrac{1}{3}\right)^2\right]^6:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left(\dfrac{1}{9}\right)^6:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left(\dfrac{1}{9}\right)^{-4}=6561\)
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a,2.(dfrac{1}{4}+x)^3(-dfrac{27}{4})b,(x+dfrac{1}{2})^3:3dfrac{-1}{81}c,(dfrac{2}{3}-x)^21:dfrac{4}{9}d,(2x-dfrac{1}{5})^2+dfrac{16}{25}1e,(dfrac{2}{5}-3x)^2-dfrac{1}{5}dfrac{4}{25}
Đọc tiếp
a,2.(\(\dfrac{1}{4}\)+x)\(^3\)=(\(-\dfrac{27}{4}\))
b,(x+\(\dfrac{1}{2}\))\(^3\):3=\(\dfrac{-1}{81}\)
c,(\(\dfrac{2}{3}\)-x)\(^2\)=1:\(\dfrac{4}{9}\)
d,(2x-\(\dfrac{1}{5}\))\(^2\)+\(\dfrac{16}{25}\)=1
e,(\(\dfrac{2}{5}\)-3x)\(^2\)-\(\dfrac{1}{5}\)=\(\dfrac{4}{25}\)
