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\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a-b}{c-d}\Rightarrow\dfrac{a}{c}.\dfrac{b}{d}=\dfrac{a-b}{c-d}.\dfrac{a-b}{c-d}\)
hay \(\dfrac{ab}{cd}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\) (đpcm)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\).Chứng minh\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}=\dfrac{ab}{cd}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng minh rằng \(\dfrac{ab}{cd}=\dfrac{\left(a+b\right)^2}{\left(c+d\right)^2}\) ( với giả thiết các tỉ số đều có nghĩa )
Cho \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\). Chứng minh rằng:\(\dfrac{ab}{cd}\)=\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
a) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) (\(a,b,c,d\ne0\)). Chứng minh rằng:
1) \(\dfrac{2a+5b}{3a-4b}=\dfrac{2c+5d}{3c-4d}\)
2) \(\dfrac{ab}{cd}=\dfrac{a^2+b^2}{c^2+d^2}\)
3) \(\dfrac{a^3+b^3}{c^3+d^3}=\dfrac{\left(a+b\right)^3}{\left(c+d\right)^3}\) \(\left(\dfrac{a}{b}=\dfrac{c}{d}\ne1\right)\)
b)Cho \(\dfrac{2a+13b}{3a-7b}=\dfrac{2c+13d}{3c-7d}\). Chứng minh rằng:\(\dfrac{a}{b}=\dfrac{c}{d}\)
c)Cho \(\dfrac{cy-bz}{x}=\dfrac{az-cx}{y}=\dfrac{bx-ay}{z}\). Chứng minh rằng: \(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)
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 \(\dfrac{a}{b}=\dfrac{c}{d}.CMR:\)
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 a/b = c/d, cmr: \(\dfrac{ab}{cd}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
1) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh rằng \(\dfrac{2a^2-3ab+5b^2}{2a^2+3ab}=\dfrac{2c^2-3cd+5d^2}{2c^2+3cd}\)
2) Cho \(\dfrac{a}{c}=\dfrac{c}{b}\). Chứng minh rằng \(\dfrac{b^2-c^2}{a^2+c^2}=\dfrac{b-a}{a}\)
3) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\).Chứng minh rằng\(\dfrac{3a^6+c^6}{3b^6+d^6}=\dfrac{\left(a+c\right)^6}{\left(b+d\right)^6}\)
Biết \(\dfrac{a}{b}< \dfrac{c}{d}\left(b,d>0\right)\)
CMR \(\dfrac{a}{b}=\dfrac{ab+cd}{b^2+d^2}< \dfrac{c}{d}\)
