Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow\dfrac{a}{c}=\dfrac{b}{d}=t\)
\(\left\{{}\begin{matrix}\dfrac{ab}{cd}=t^2\\\dfrac{a^2}{c^2}=\dfrac{b^2}{d^2}=\dfrac{a^2-b^2}{c^2-d^2}=t^2\end{matrix}\right.\)
Ta có đpcm
Cho \(\dfrac{a}{b}=\dfrac{c}{d}.CMR:\)
a, \(\dfrac{a^2-b^2}{ab}=\dfrac{c^2-d^2}{cd}\)
b, \(\dfrac{\left(a+b\right)^2}{a^2+b^2}=\dfrac{\left(c+d\right)^2}{c^2+d^2}\)
Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh rằng ta có các tỉ lệ thức sau (giả thiết các tỉ lệ thức là có nghĩa ) :
a) \(\dfrac{ab}{cd}=\dfrac{a^2-b^2}{c^2-d^2}\)
b) \(\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2+b^2}{c^2+d^2}\)
Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}.CMR:\dfrac{ab}{cd}=\dfrac{a^2-b^2}{c^2-d^2}\)
Cho \(\dfrac{a}{b}< \dfrac{c}{d}\)và b, d > 0 . CMR : \(\dfrac{a}{b}< \dfrac{ab+cd}{b^2+d^2}< \dfrac{c}{d}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\).Chứng minh\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}=\dfrac{ab}{cd}\)
cho a/b = c/d, cmr: \(\dfrac{ab}{cd}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
biết:\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}\) với a,b,c,d\(\ne\)0. CMR:
\(\dfrac{a}{b}=\dfrac{c}{d}\) hoặc \(\dfrac{a}{b}=\dfrac{d}{c}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) chứng minh rằng:
a) \(\dfrac{ab}{cd}=\dfrac{a^2+b^2}{c^2+d^2}\)
b)\(\dfrac{ac}{bd}=\dfrac{a^2+c^2}{b^2+d^2}\)
c)\(\dfrac{7a^2-3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)
Cho tỉ lệ thức \(\dfrac{a}{b}\) = \(\dfrac{c}{d}\) . CM các tỉ lệ thức sau :
a. \(\dfrac{a^2-b^2}{ab}\) = \(\dfrac{c^2-d^2}{cd}\)
b. \(\dfrac{(a+b)^2}{a^2+b^2}\) =\(\dfrac{(c+d)^2}{c^2+d^2}\)
