Các câu hỏi tương tự
1/ Biết frac{a}{b}frac{c}{d}, chứng minha) frac{a^2+b^2}{c^2+d^2}frac{left(a+bright)^2}{left(c+dright)^2}b) left(frac{a-d}{c-b}right)^4frac{a^4+b^4}{c^4+d^4}2/ Cho frac{a}{b}frac{b}{c}frac{c}{d}Chứng minh left(frac{a+b+c}{b+c+d}right)^3frac{a}{b}3/ Cho frac{a}{b}frac{b}{c}frac{c}{d}Chứng minh abc
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1/ Biết \(\frac{a}{b}=\frac{c}{d}\), chứng minh
a) \(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b) \(\left(\frac{a-d}{c-b}\right)^4=\frac{a^4+b^4}{c^4+d^4}\)
2/ Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)
Chứng minh \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{b}\)
3/ Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)
Chứng minh a=b=c
Cho \(\frac{a}{b}\)=\(\frac{c}{d}\)
CM: A, \(\frac{a^2+b^2}{c^2+d^2}\)=\(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
B, \(\frac{\left(a-b\right)^2}{\left(c-d\right)^2}\)=\(\frac{a^4+b^4}{c^4+d^4}\)
Chofrac{a}{b}frac{c}{d} chứng minh 1,frac{a^2+c^2}{b^2+d^2}frac{a.c}{b.d} 2,frac{a^2+c^2}{b^2+d^2}frac{a^2-c^2}{b^2-d^2} 3,left(a+cright).left(b-dright)left(a-cright).left(b+dright) 4,left(b+dright).cleft(c+cright).d 5,frac{4.a-12.b}{8.a+11.b}frac{4.c-12.d}{8.c+11.d} 6,frac{left(a+cright)^2}{left(b+dright)^2}frac{left(a+cright)^2}{left(b+dright)^2} 7,frac{a^{10}+b^{10}}{left(a+bright)^{10}}frac{c^{10}+d^{10}}{left(c+dright)^{10}}
Đọc tiếp
Cho\(\frac{a}{b}\)=\(\frac{c}{d}\) chứng minh
1,\(\frac{a^2+c^2}{b^2+d^2}\)=\(\frac{a.c}{b.d}\)
2,\(\frac{a^2+c^2}{b^2+d^2}\)=\(\frac{a^2-c^2}{b^2-d^2}\)
\(3,\left(a+c\right).\left(b-d\right)=\left(a-c\right).\left(b+d\right)\)
\(4,\left(b+d\right).c=\left(c+c\right).d\)
\(5,\frac{4.a-12.b}{8.a+11.b}=\frac{4.c-12.d}{8.c+11.d}\)
\(6,\frac{\left(a+c\right)^2}{\left(b+d\right)^2}=\frac{\left(a+c\right)^2}{\left(b+d\right)^2}\)
\(7,\frac{a^{10}+b^{10}}{\left(a+b\right)^{10}}=\frac{c^{10}+d^{10}}{\left(c+d\right)^{10}}\)
Cho \(\frac{a}{b}\)= \(\frac{c}{d}\)CMR
a) \(\frac{a^2+b^2}{a^2+d^2}\)= \(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b) \(\left(\frac{a-b}{c-d}\right)^4\)= \(\frac{a^4+b^4}{c^4+d^4}\)
Cho \(\frac{a}{b}\)= \(\frac{c}{d}\) CMR:
a) \(\frac{a^2+b^2}{a^2+d^2}\)= \(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b) \(\left(\frac{a-b}{c-d}\right)^4\)= \(\frac{a^4+b^4}{c^4+d^4}\)
Cho tỉ lệ thức frac{a}{b}frac{c}{d}C/m:a)frac{a+b}{b}frac{c+d}{d}b)frac{â-b}{b}frac{c-d}{d}c)frac{a+b}{a}frac{c+d}{c}d)frac{a-b}{a}frac{c-d}{c}e)frac{a}{a+b}frac{c}{c+d}f)frac{a}{a-b}frac{c}{c-d}g)frac{a^2+b^2}{c^2+d^2}frac{left(a+bright)^2}{left(c+dright)^2}h)frac{left(a-bright)^2}{left(c-dright)^2}frac{a^4+b^4}{c^4+d^4}( áp dụng t/c tỉ lệ thức và dãy tỉ số nhau)
Đọc tiếp
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)C/m:
a)\(\frac{a+b}{b}=\frac{c+d}{d}\)
b)\(\frac{â-b}{b}=\frac{c-d}{d}\)
c)\(\frac{a+b}{a}=\frac{c+d}{c}\)
d)\(\frac{a-b}{a}=\frac{c-d}{c}\)
e)\(\frac{a}{a+b}=\frac{c}{c+d}\)
f)\(\frac{a}{a-b}=\frac{c}{c-d}\)
g)\(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
h)\(\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{a^4+b^4}{c^4+d^4}\)
( áp dụng t/c tỉ lệ thức và dãy tỉ số = nhau)
cho a, b, c, d la 4 so nguyen duong thoa man: b= \(\frac{a+c}{2}va\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{b}+\frac{1}{d}\right)\)
chung minh: \(\frac{a}{b}=\frac{c}{d}\)
Cho:
\(\frac{a}{b}=\frac{c}{d}\left(b\ne d\right)\)
Chứng minh a/
\(\frac{\left(a-c\right)^4}{\left(b-d\right)^4}=\frac{5a^4+7c^4}{5b^4+7d^4}\)
b/
\(\frac{ac}{bd}=\frac{5a^2+7c^2}{5b^2+7d^2}\)
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...
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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)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)