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\(Q=1985\times\frac{x^3}{3}+1979\times\frac{x^2}{2}+5\times\frac{x}{6}\)
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DD
2
KT
11 tháng 7 2018
Bài 1:
a) \(\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}\)
\(=\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\frac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)
\(=\frac{2\left(\sqrt{3}+1\right)}{2}-\frac{2\left(\sqrt{3}-1\right)}{2}\)
\(=\sqrt{3}+1-\left(\sqrt{3}-1\right)=2\)
b) \(\frac{2}{5-\sqrt{3}}+\frac{3}{\sqrt{6}+\sqrt{3}}\)
\(=\frac{2\left(5+\sqrt{3}\right)}{\left(5-\sqrt{3}\right)\left(5+\sqrt{3}\right)}+\frac{3\left(\sqrt{6}-\sqrt{3}\right)}{\left(\sqrt{6}+\sqrt{3}\right)\left(\sqrt{6}-\sqrt{3}\right)}\)
\(=\frac{2\left(5+\sqrt{3}\right)}{2}+\frac{3\left(\sqrt{6}-\sqrt{3}\right)}{3}\)
\(=5+\sqrt{3}+\sqrt{6}-\sqrt{3}=5+\sqrt{6}\)
c) ĐK: \(a\ge0;a\ne1\)
\(\left(1+\frac{a+\sqrt{a}}{1+\sqrt{a}}\right).\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)+a\)
\(=\left(1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{1+\sqrt{a}}\right).\left(1-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)+a\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)+a\)
\(=1-a+a=1\)
IA
25 tháng 3 2020
1, =\(\frac{2\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}=\frac{1}{2}\)
2, A=\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{99}{100}\)
= \(\frac{1\cdot2\cdot3\cdot....\cdot99}{2\cdot3\cdot4\cdot...\cdot100}=\frac{1}{100}\)
Vậy ......
hok tốt
TM
26 tháng 1 2017
\(A=\left(\frac{1}{x-1}-\frac{x}{1-x^3}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\left(\frac{1}{x-1}-\frac{x}{\left(1-x\right)\left(1+x+x^2\right)}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\left(\frac{1}{x-1}-\frac{x}{\left(1-x\right)\left(x+1\right)}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\left(\frac{-x-1}{\left(1-x\right)\left(x+1\right)}-\frac{x}{\left(1-x\right)\left(x+1\right)}\right):\frac{2x+1}{x^2+2x+1}\)
\(A=\frac{-2x-1}{\left(1-x\right)\left(x+1\right)}:\frac{2x+1}{x^2+2x+1}\)
\(A=\frac{-\left(2x+1\right)}{\left(1-x\right)\left(x+1\right)}.\frac{\left(x+1\right)^2}{2x+1}\)
\(A=\frac{-1}{1-x}.\frac{x+1}{1}\)
\(A=\frac{-x-1}{1-x}\)
25 tháng 5 2016
A=3/4x8/9x15/16x24/25x...x899/900
A=1.3/22 x 2.4/33 x 3.5/42 x 4.6/55 x ... x 29.31/302
A=1.2.3.4...29/2.3.4.5...30 x 3.4.5.6...31/2.3.4.5...30
A=1/30 x 31/2
A=31/60