\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a^2+c^2}{b^2+d^2}=\frac{a}{b}.\frac{c}{d}=\frac{ac}{bd}\)
Vậy \(\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\)
Có a/b=c/d chứng minh rằng \(\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a.c}{b.d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\) chứng minh :
\(\frac{a.c}{b.d}=\frac{a^2+c^2}{b^2+c^2}\)
cho \(\frac{a}{b}\)= \(\frac{c}{d}\)chứng minh rằng:
a) \(\frac{a}{3a+b}=\frac{c}{3c+d}\)
b)\(\frac{a.c}{b.d}=\frac{a^2+c^2}{b^2+d^2}\)
c) \(\frac{a.b}{c.d}=\frac{a^2-b^2}{c^2-d^2}\)
Cho \(\frac{a}{b}\)=\(\frac{c}{d}\)chứng minh rằng
a)\(\frac{a}{a-b}\)=\(\frac{c}{c-d}\)
b)\(\frac{a}{b}=\frac{a+c}{b+d}\)
c)\(\frac{a}{3a+b}=\frac{c}{3c+d}\)
d)\(\frac{a.c}{b.d}=\frac{a^2+c^2}{b^2+d^2}\)
f)\(\frac{a.b}{c.d}=\frac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
Cho tỉ lệ thức \(\frac{a}{b}\)= \(\frac{c}{d}\)chứng minh rằng \(\frac{a.c}{b.d}\)=\(\frac{2009.a^2+2010.c^2}{2009.b^2+2010.d^2}\)
Cho \(\frac{a}{b}=\frac{c}{d}\)
Chứng minh rằng : \(\frac{a.c}{b.d}=\frac{a^2+c^2}{b^2+d^2}\)
Giải = cách đặt k nhé :))
Chứng minh rằng \(\frac{a}{b}=\frac{c}{d}\) biết:
a) \(\frac{a}{a-b}=\frac{c}{c-d}\) b)\(\frac{a.c}{b.d}=\frac{a^2+c^2}{b^2+d^2}\)
c) \(\frac{a.b}{c.d}=\frac{a^2-b^2}{c^2-d^2}\)
Cho tỉ lệ thức \(\frac{a}{b}\)+ \(\frac{c}{d}\)Chứng minh rằng \(\frac{a.c}{b.a}\)= \(\frac{a^2.b^2}{b^2+d^2}\)
Bài 1: Cho
\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)
Chứng minh: \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
Bài 2: Cho
\(\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}\)
Tính giá trị của \(\frac{a}{b+c};\frac{b}{c+a};\frac{c}{a+b}\)
Bài 3: Tìm x,y biết:
\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}\)
Bài 4: Tìm a,b,c:
a, \(a.b=\frac{3}{5};b.c=\frac{4}{5};c.a=\frac{3}{4}\)
b, a.(a+b+c)= -12
b.(a+b+c)= 18
c.(a+b+c)= 30
c, a.b=c; b.c= 4a; a.c= 9b
