Các câu hỏi tương tự
1/ cho \(\frac{a}{b}=\frac{c}{d}\)chứng minh rằng:
a) \(\frac{a.b}{c.d}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b)\(\frac{a,d}{c.b}=\frac{\left(a+b\right).\left(a-b\right)}{\left(c+d\right).\left(c-d\right)}\)
2/ cho \(a.b=c^2\)chứng minh : \(\frac{a}{b}=\frac{\left(2a+3c\right)^2}{\left(2c+3b\right)^2}\)
Cho\(\frac{a}{b}=\frac{c}{d};\left(a,b,c,d,\right)\)chứng minh\(\frac{a.b}{c.d}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
Cho biết a+c=2b;và 2bd=c(b+d) , chứng minh rằng: \(2\left(\frac{10a+c}{10b+d}\right)^2-\left(\frac{a}{b}\right)^2=\left(\frac{c}{d}\right)^2\)
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}}
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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}. 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)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)
\(\frac{2x-3y}{2}=\frac{4y-2z}{3}=\frac{3z-4x}{4}\) và 3x +2y+z=17
Cho \(\frac{a}{b}=\frac{c}{d}\)chứng minh rằng
\(\frac{ab}{cd}=\frac{\left(a-b\right)^2}{\left(c-d^2\right)}=\frac{\left(a+b^2\right)}{\left(c+d\right)^2}\)
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
\(\frac{a}{b}=\frac{c}{d}\)(a,b,c,d khác 0)
Chứng minh :\(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
CÁC BÀI TẬP DẠNG CHỨNG MINH TỈ LỆ THỨCBÀI 1: Cho frac{a}{b}frac{b}{d}Chứng minh frac{a^2+b^2}{b^2+d^2}frac{a}{d}Bài 2: Cho frac{a}{b}frac{b}{c}frac{c}{d} Chứng minh left(frac{â+b+c}{b+c+d}right)^3frac{a}{d}Bài 3: Cho frac{a}{2015}frac{b}{2016}frac{c}{2017} Chứng minh frac{left(a-cright)^2}{left(a-bright).left(b-cright)}4
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CÁC BÀI TẬP DẠNG CHỨNG MINH TỈ LỆ THỨC
BÀI 1: Cho \(\frac{a}{b}=\frac{b}{d}\)Chứng minh \(\frac{a^2+b^2}{b^2+d^2}\)=\(\frac{a}{d}\)
Bài 2: Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\) Chứng minh \(\left(\frac{â+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
Bài 3: Cho \(\frac{a}{2015}=\frac{b}{2016}=\frac{c}{2017}\) Chứng minh \(\frac{\left(a-c\right)^2}{\left(a-b\right).\left(b-c\right)}=4\)