Question

cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)

CMRa)\(\frac{ab}{cd}=\)\(\frac{a^2-b}{c^{^2}-d^2}\)

Answer 1

đề sai \(\frac{ab}{cd}=\frac{a^2-b^2}{c^2-d^2}\)

Answer 2

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)

\(\Rightarrow a=bk;c=dk\)

\(\Rightarrow VT=\frac{ab}{cd}=\frac{bkb}{dkd}=\frac{b^2k}{d^2k}=\frac{b^2}{d^2}\left(1\right)\)

\(\Rightarrow VP=\frac{\left(bk\right)^2-b^2}{\left(dk\right)^2-d^2}=\frac{b^2k^2-b^2}{d^2k^2-d^2}=\frac{b^2\left(k^2-1\right)}{d^2\left(k^2-1\right)}=\frac{b^2}{d^2}\left(2\right)\)

Từ (1) và (2) =>Đpcm