Question

cho a/b = c/d chứng minh rằng

a²/b² = 3a² - 2ac/3b² - 2bc

Answer 1

Đặt a/b=c/d=k

=>a=bk; c=dk

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

\(\dfrac{3a^2-2ac}{3b^2-2bd}=\dfrac{3\cdot b^2k^2-2\cdot bk\cdot dk}{3b^2-2bk}=k^2\)

Do đó: \(\dfrac{a^2}{b^2}=\dfrac{3a^2-2ac}{3b^2-2bd}\)