Question

1) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) và a, b, c, d khác 0. CMR : a) \(\dfrac{a^2}{c^2}=\dfrac{2a^2+3b^2}{2c^2+2d^2}\) b) \(\dfrac{2a-3c}{c}=\dfrac{2b-2d}{d}\)

2) Cho \(\dfrac{4x-5y}{3}=\dfrac{5z-3x}{4}=\dfrac{3y-4z}{6}\). CMR: \(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{3}\)

Giúp mình với nha! :)))))

Answer 1

Câu 1:

Đặt a/b=c/d=k

=>a=bk; c=dk

a: \(\dfrac{a^2}{c^2}=\dfrac{b^2k^2}{d^2k^2}=\dfrac{b^2}{d^2}\)

\(\dfrac{2a^2+3b^2}{2c^2+3d^2}=\dfrac{2b^2k^2+3b^2}{2d^2k^2+3d^2}=\dfrac{b^2}{d^2}\)

=>\(\dfrac{a^2}{c^2}=\dfrac{2a^2+3b^2}{2c^2+3d^2}\)

b: \(\dfrac{2a-3c}{c}=\dfrac{2bk-3dk}{dk}=\dfrac{2b-3d}{d}\)