Question

Từ tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\) suy ra (coi các biểu thức đều xác định) :

\(\frac{ad}{bc}=\frac{a^2}{b^2}\)

\(\frac{a^2}{b^2}=\frac{ac}{bd}\)

\(\frac{a}{b}=\frac{c^2}{d^2}\)

\(\frac{ad}{bc}=\frac{c^2}{d^2}\)

Answer 1

Ta có: \(\frac{a}{b}\)=\(\frac{c}{d}\)

+ \(\frac{a}{b}\)=\(\frac{a}{b}\).\(\frac{a}{b}\)=\(\frac{a^2}{b^2}\) (1)

+ \(\frac{a}{b}\)=\(\frac{c}{d}\)=\(\frac{ac}{bd}\) (2)

Từ (1); (2) => \(\frac{a}{b}\)=\(\frac{c}{d}\)=>\(\frac{a^2}{b^2}\)=\(\frac{ac}{bd}\)

Answer 2

Ta có \(\frac{a}{b}=\frac{c}{d}\Rightarrow\left(\frac{a}{b}\right)^2=\frac{a^2}{b^2}=\left(\frac{c}{d}\right)^2=\frac{a.c}{b.d}\left(ĐPCM\right)\)

 

Answer 3

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