A= [3/2-(x^4-x^4+1/x^2+1)*x^2-x(4*x-1)-4/x^7+6*x^4-x-6]/x^3+29*x+78/3*x^2+12*x-36.rut gon
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1.a) (2 + 1)(22 + 1)((24 + 1)(28 + 1) = (22 - 1)(22 + 1)(24 + 1)(28 + 1) = (24 - 1)(24 + 1)(28 + 1)
= (28 - 1)(28 + 1) = 216 - 1
b) 7(23 + 1)(26 + 1)(212 + 1)(224 + 1) = (23 - 1)(23 + 1)(26 + 1)(212 + 1)(224 + 1)
= (26 - 1)(26 + 1)(212 + 1)(224 + 1) = (212 - 1)(212 + 1)(224 + 1) = (224 - 1)(224 + 1) = 248 - 1
c) (x2 - x + 1)(x2 + x + 1)(x2 - 1) = [(x2 - x + 1)(x + 1)][(x2 + x + 1)(x - 1)] = (x3 + 1)(x3 - 1) = x6 - 1
2. Đặt A = 4x - x2 - 1 = -(x^2 - 4x + 4) + 3 = -(x - 2)2 + 3 \(\le\)3 \(\forall\)x
Dấu "=" xảy ra <=> x - 2 = 0 <=> x = 2
Vậy MaxA = 3 khi x = 2
1) \(A=\frac{7}{10\times11}+\frac{7}{11\times12}+\frac{7}{12\times13}+...+\frac{7}{69\times70}\)
\(A=7\times\left(\frac{1}{10\times11}+\frac{1}{11\times12}+\frac{1}{12\times13}+...+\frac{1}{69\times70}\right)\)
\(A=7\times\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(A=7\times\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(A=7\times\frac{3}{35}\)
\(A=\frac{3}{5}\)
2) \(B=\frac{1}{25\times27}+\frac{1}{27\times29}+\frac{1}{29\times31}+...+\frac{1}{73\times75}\)
\(B=\frac{1}{2}\times\left(\frac{2}{25\times27}+\frac{2}{27\times29}+\frac{2}{29\times31}+...+\frac{2}{73\times75}\right)\).
\(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\times\frac{2}{75}\)
\(B=\frac{1}{75}\)
3) \(C=\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+...+\frac{4}{2008\times2010}\)
\(C=\frac{4}{2}\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+...+\frac{2}{2008\times2010}\right)\)
\(C=2\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(C=2\times\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(C=2\times\frac{502}{1005}\)
\(C=\frac{1004}{1005}\)
_Chúc bạn học tốt_
1) 3/4 : x/6 = 75/100
x/6 = 3/4 : 75/100
x/6 = 1
x = 1*6
x = 6
Câu 6: Bạn xem ở đây: http://olm.vn/hoi-dap/question/615090.html
1.\(\frac{3}{4}:\frac{x}{6}=\frac{75}{100}\) \(\Leftrightarrow\frac{3}{4}.6.\frac{1}{x}=\frac{3}{4}\)
\(\Leftrightarrow\frac{6}{x}=1\)
\(\Leftrightarrow x=\frac{1}{6}\)