Question

Cmr: \(\frac{a}{b}\)=\(\frac{c}{d}\) thì \(\frac{a^2+b^2}{c^2+d^2}\)=\(\frac{ab}{cd}\)

Answer 1

Có \(\frac{a}{b}=\frac{c}{d}\)

=> \(\frac{a}{c}=\frac{b}{d}\)

\(=>\left(\frac{a}{c}\right)^2=\left(\frac{b}{d}\right)^2=\frac{ac}{bd}\)

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

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

Vậy =>đpcm

Answer 2

Nguyễn Tuấn Minh giải sai rồi bạn ơi

Answer 3

\(\frac{a}{b}=\frac{c}{d}.Đặt:a=bk;c=dk\)

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

\(\frac{ab}{cd}=\frac{bkb}{dkd}=\frac{b^2k}{d^2k}=\frac{b^2}{d^2}\Rightarrow\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\left(dpcm\right)\)