ta có: (a+b+c+d).(a-b-c+d)=(a-b+c-d).(a+b-c-d)
<=> a2-ab-ac+ad+ab-b2-bc+bd+ac-bc-c2+cd+ad-bd-cd+d2=a2+ab-ac-ad-ab-b2+bc+bd+ac+bc-c2-cd-ad-bd+cd+d2
<=> a2-b2-c2+d2+2ad-2bc=a2-b2-c2+d2-2ad+2bc
<=> 2ad-2bc=-2ad+2bc
<=> ad=bc
<=> a/b = c/d (dpcm)
Cho \(\frac{a}{b}\) = \(\frac{c}{d}\) chứng minh :
a) \(\frac{a^2 + b^2}{c^2 + d^2}\) = \(\frac{a*b}{c*d}\)
b) \(frac{(a + b)^2}{(c + d)^2}\) = \(\frac{a*b}{c*d}\)
a/Cho biết \(\frac{a+b}{a-b}\)=\(\frac{c+d}{c-d}\).Chứng minh rằng \(\frac{a}{b}\)=\(\frac{c}{d}\)
b/Cho biết (a+b+c+d)(a-b-c-d)=(a-b+c-d)(a+b-c-d) Chứng minh rằng \(\frac{a}{b}\)=\(\frac{c}{d}\)
cho a;b;c;d thỏa mãn: \(\frac{a+b-c}{d}=\frac{b+c-d}{a}=\frac{c+d-a}{b}=\frac{d+a-b}{c}\)
Chứng minh : \(\frac{a+b}{c+d}=\frac{b+c}{d+a}=\frac{c+d}{a+b}\)
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
a) cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
i) \(\frac{a}{a+b}\frac{c}{c+d}\)
ii)\(\frac{a-b}{c-d}=\frac{a+c}{b+d}.\)
b) Cho: \(\frac{2a+b}{a-2b}=\frac{2c+d}{c-2d}\). Chứng minh: \(\frac{a}{b}=\frac{c}{d}.\)
Cho ( a+b+c+d ) ( a-b-c+d ) = ( a-b+c-d ) ( a+b-c-d )
Chứng minh rằng \(\frac{a}{b}=\frac{c}{d}\)
Cho \(a,b,c,d>0\). Chứng minh rằng:\(1< \frac{a}{a+b+c}+\frac{b}{b+c+d}+\frac{c}{c+d+a}+\frac{d}{d+a+b}< 2\).
Cho (a+b+c+d).(a-b-c+d)=(a-b+c-d).(a+b-c-d)
Chứng minh \(\frac{a}{b}=\frac{c}{d}\)
Chứng minh rằng ta có tỉ lệ thức: \(\frac{a}{b}=\frac{c}{d}\)
a)\(\frac{a+b}{a-b}=\frac{c+d}{c-d}\)
b) (a+b+c+d).(a-b-c-d)=(a-b+c-d).(a+b-c-d)
