Đặt \(\dfrac{a}{2007}=\dfrac{b}{2008}=\dfrac{c}{2009}=k\)
=>a=2007k; b=2008k; c=2009k
\(4\left(a-b\right)\left(b-c\right)=4\left(2007k-2008k\right)\left(2008k-2009k\right)\)
\(=4\cdot\left(-k\right)\cdot\left(-k\right)=4k^2\)
\(\left(c-a\right)^2=\left(2009k-2007k\right)^2=4k^2\)
Do đó: \(4\left(a-b\right)\left(b-c\right)=\left(c-a\right)^2\)
Tính hợp lý:
a, \(2008\cdot\left(\dfrac{1}{2007}-\dfrac{2009}{1004}\right)-2009\cdot\left(\dfrac{1}{2007}-2\right)\)
b,\(\dfrac{5^5\cdot20^3-5^4\cdot20^3+5^7\cdot4^5}{\left(20+5\right)^3\cdot4^5}\)
tính hợp lý :
a, \(2008.\left(\dfrac{1}{2007}-\dfrac{2009}{1004}\right)-2009.\left(\dfrac{1}{2007}-2\right)\)
b, \(\dfrac{5^5.20^3-5^4.20^3+5^7.4^5}{\left(20+5\right)^3.4^5}\)
Bài 1. a, Cho A = \(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right).....\left(\dfrac{1}{10}-1\right)\)
So sánh A với \(\dfrac{-1}{9}\)
Bài 2. Cho A = \(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)....\left(\dfrac{1}{2008}-1\right)\left(\dfrac{1}{2009}-1\right)\)
B = \(\left(-1\dfrac{1}{2}\right)\left(-1\dfrac{1}{3}\right)....\left(-1\dfrac{1}{2007}\right)\left(-1\dfrac{1}{2008}\right)\)
Tính A . B ?
Bài 1 : Cho các số thực a,b,c khác 0 thỏa mãn \(a+b+c=2;a^2+b^2+c^2=4\) và \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\)
Chứng minh rằng : xy+yz+zx=0
Bài 2 : Cho x khác -1;0;1 thỏa mãn \(\dfrac{a}{x-1}=\dfrac{b}{x}=\dfrac{c}{x+1}\) Chứng minh rằng : \(4\left(a-b\right)\left(b-c\right)=\left(a-c\right)^2\)
Bài 3 : Cho các số thực a,b,c khác 0 thỏa mãn \(\dfrac{x}{a+2b-c}=\dfrac{y}{2a+b+c}=\dfrac{z}{4b+c-4a}\) . Chứng minh rằng : \(\dfrac{a}{x+2y-z}=\dfrac{b}{2x+b+c}=\dfrac{c}{4y+z-4x}\)
GIÚP MÌNH ĐI CHIỀU 1 GIỜ ĐI HOK RỒI !!!
Tính tỉ số \(\dfrac{A}{B}\) , biết:
\(A=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}\)
\(B=\dfrac{2008}{1}+\dfrac{2007}{2}+\dfrac{2006}{3}+...+\dfrac{2}{2007}+\dfrac{1}{2008}\)
1) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh rằng \(\dfrac{2a^2-3ab+5b^2}{2a^2+3ab}=\dfrac{2c^2-3cd+5d^2}{2c^2+3cd}\)
2) Cho \(\dfrac{a}{c}=\dfrac{c}{b}\). Chứng minh rằng \(\dfrac{b^2-c^2}{a^2+c^2}=\dfrac{b-a}{a}\)
3) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\).Chứng minh rằng\(\dfrac{3a^6+c^6}{3b^6+d^6}=\dfrac{\left(a+c\right)^6}{\left(b+d\right)^6}\)
a) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) (\(a,b,c,d\ne0\)). Chứng minh rằng:
1) \(\dfrac{2a+5b}{3a-4b}=\dfrac{2c+5d}{3c-4d}\)
2) \(\dfrac{ab}{cd}=\dfrac{a^2+b^2}{c^2+d^2}\)
3) \(\dfrac{a^3+b^3}{c^3+d^3}=\dfrac{\left(a+b\right)^3}{\left(c+d\right)^3}\) \(\left(\dfrac{a}{b}=\dfrac{c}{d}\ne1\right)\)
b)Cho \(\dfrac{2a+13b}{3a-7b}=\dfrac{2c+13d}{3c-7d}\). Chứng minh rằng:\(\dfrac{a}{b}=\dfrac{c}{d}\)
c)Cho \(\dfrac{cy-bz}{x}=\dfrac{az-cx}{y}=\dfrac{bx-ay}{z}\). Chứng minh rằng: \(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)
Tìm x :
a) \(3-\dfrac{2}{2x-3}=\dfrac{2}{5}+\dfrac{1}{2x-3}-\dfrac{3}{2}\)
b) \(7.\left(x.1\right)+2x.\left(1-x\right)=0\)
c) \(\dfrac{x+1}{2018}+\dfrac{x+2}{2017}+\dfrac{x+3}{2016}=\dfrac{x+10}{2009}+\dfrac{x+11}{2008}+\dfrac{x+12}{2007}\)
Có 3 ý thui các bạn hãy giúp mk!!!!!!
Cho a,b,c,d là 4 số khác 0; biết \(\dfrac{a}{b}=\dfrac{c}{d}\).Chứng minh rằng \(\dfrac{a^{2017}+b^{2017}}{c^{2017}+d^{2017}}=\dfrac{\left(a-b\right)^{2017}}{\left(c-d\right)^{2017}}\)
