Question

Cho a/b=c/d. CMR:

1) a² /c²=2a² + 3b²/ 2c²+3d²

2) 2a - 3c/c = 2b-3d/d

Answer 1

1) \(\frac{a}{b}=\frac{c}{d}\)\(\Rightarrow\frac{a}{c}=\frac{b}{d}\)

\(\Rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{2a^2}{2c^2}=\frac{3b^2}{3d^2}\)\(=\frac{2a^2+3b^2}{2c^2+3d^2}\)( theo tính chất dãy tỉ số bằng nhau )

\(\Rightarrow\frac{a^2}{c^2}=\frac{2a^2+3b^2}{2c^2+3d^2}\)

2) \(\frac{a}{b}=\frac{c}{d}\)\(=\frac{2a}{2b}=\frac{3c}{3d}=\frac{2a-3c}{2b-3d}\)( theo tính chất dãy tỉ số bằng nhau )

\(\Rightarrow\frac{2a-3c}{2b-3d}=\frac{c}{d}\)\(\Rightarrow\frac{2a-3c}{c}=\frac{2b-3d}{d}\)