Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\)

Chứng minh \(\dfrac{a^2}{b^2}=\dfrac{2c^2-ac}{2d^2-bd}\)

Answer 1

Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{a^2}{b^2}\) (1)

Lại có: \(\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{a^2}{b^2}=\dfrac{a}{b}.\dfrac{a}{b}=\dfrac{a}{b}.\dfrac{c}{d}=\dfrac{ac}{bd}=\dfrac{c^2}{d^2}=\dfrac{2c^2}{2d^2}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\Rightarrow\dfrac{a}{b}=\dfrac{c}{d}=\dfrac{2c^2-ac}{2d^2-bd}\) (2)

Từ (1) và (2) \(\Rightarrow\dfrac{a^2}{b^2}=\dfrac{2c^2-ac}{2d^2-bd}\).