Các câu hỏi tương tự
Cho frac{a}{b}frac{c}{d}. Chứng minh:a) frac{left(a-bright)^3}{left(c-dright)^3}frac{3a^2+2b^2}{3c^2+2d^2}b)frac{4a^4+5b^4}{4c^4+5d^4}frac{a^2b^2}{c^2d^2}c)left(frac{a-b}{c-d}right)^{2005}frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}d)frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}frac{left(a+bright)^{2005}}{left(c+dright)^{2005}}e)frac{left(20a^{2006}+11b^{2006}right)^{2007}}{left(20a^{2007}-11b^{2007}right)^{2006}}frac{left(20c^{2006}+11d^{2006}right)^{2007}}{left(20c^{2007}-11d^{2007}right)^{20...
Đọc tiếp
Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
a) \(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
b)\(\frac{4a^4+5b^4}{4c^4+5d^4}=\frac{a^2b^2}{c^2d^2}\)
c)\(\left(\frac{a-b}{c-d}\right)^{2005}=\frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}\)
d)\(\frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}=\frac{\left(a+b\right)^{2005}}{\left(c+d\right)^{2005}}\)
e)\(\frac{\left(20a^{2006}+11b^{2006}\right)^{2007}}{\left(20a^{2007}-11b^{2007}\right)^{2006}}=\frac{\left(20c^{2006}+11d^{2006}\right)^{2007}}{\left(20c^{2007}-11d^{2007}\right)^{2006}}\)
f)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)
Chứng minh rằng :
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}=\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}_{ }\)
\(\frac{a+2006}{a-2006}=\frac{b+2005}{b-2005}chứngminh\frac{a}{b}=\frac{2006}{2005}\)
Chứng minh rằng
B=\(\left[1.2.3.4.5.6...2006\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2006}\right)\right]⋮2007\)
So sánh : \(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}+\frac{2009}{2006}\)với 4
Tính:
\(A=\frac{3^3+1^3}{2^3-1^3}+\frac{5^3+2^3}{3^3-2^3}+..............+\frac{4013^3+2006^3}{2007^3-2006^3}\)
so sánh: \(\left(\frac{2006-2005}{2006+2005}\right)^2\) và \(\frac{2006^2-2005^2}{2006^2+2005^2}\)
\(\frac{x+6}{2001}+\frac{x+5}{2002}+\frac{x+4}{2003}=\frac{x+3}{2004}+\frac{x+2}{2005}\)+\(\frac{x+1}{2006}\)
Tìm x
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)Chứng minh:
a)\(\frac{\left(20a^{2006}+11b^{2006}\right)^{2007}}{\left(20a^{2007}-11b^{2007}\right)^{2006}^{ }}=\frac{\left(20c^{2006}+11d^{2006}\right)^{2007}}{\left(20c^{2007}-11d^{2007}\right)^{2006}}\)
b)\(\left(4a+5b\right)\left(7c-11d\right)=\left(7a-11b\right)\left(4c+5d\right)\)