a) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{ab}{cd}=\frac{a.a}{c.c}=\frac{b.b}{c.d}=\frac{a^2-b^2}{c^2-d^2}\)
b) \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\Rightarrow\frac{ab}{cd}=\frac{a}{c}.\frac{b}{d}=\frac{a-b}{c-d}.\frac{a-b}{c-d}=\frac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
cho \(\frac{a}{b}=\frac{c}{d}\) chứng minh rằng :\(\frac{ab}{cd}=\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
cho tỉ lệ thúc \(\frac{a}{b}=\frac{c}{d}\). Chứng minh rằng
\(a,\frac{a}{3a+b}=\frac{c}{3c+d}\)
\(b,\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{ab}{cd}\)
Cho\(\frac{a}{b}\)=\(\frac{c}{d}\),chứng minh rằng \(\frac{ab}{cd}\)=\(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
Cho \(\frac{a}{b}=\frac{c}{b}\) CM :
a )\(\left(\frac{a-b}{c-d}\right)^2=\frac{ab}{cd}\)
b ) \(\left(\frac{a+b}{c+d}\right)^3=\frac{a^3-b^3}{c^3-d^3}\)
Cho \(\frac{a}{b}=\frac{c}{d}\). CMR: \(\frac{ab}{cd}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
Tìm GTNN của:
a. A= |x| + |x-1| + |x+2|
b. B= \(x^2-5x+9\)
cho tỉ lệ thức a/b=c/d. Chứng minh rằng
\(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}=\frac{a^2+b^2}{c^2+d^2}\)
1) Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)
Chứng minh \(\frac{a}{b}=\frac{a-c}{b-d}\left(b,d\ne0\right)\)
2) Cho \(\frac{a}{b}=\frac{c}{d}\)
Chứng minh \(\frac{a+b}{a-b}=\frac{c+d}{c-d}\left(a-b\ne0;c-d\ne0\right)\)
Cho\(\frac{a}{b}=\frac{c}{d}.\) Chứng minh \(\frac{a^2-b^2}{c^2-d^2}=\frac{ab}{cd}\)
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\). Chứng tỏ tỉ lệ thức \(\frac{ac}{bd}=\frac{\left(a+c\right)^2}{\left(b+d\right)^2}\)