Question

CMR : \(\dfrac{7a^2+3ab}{11a^2-8b^2}\)=\(\dfrac{7c^2+3cd}{11d^2-8d^2}\) biết rằng \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\)

Answer 1

Từ \(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}\Rightarrow\dfrac{a^2}{c^2}=\dfrac{b^2}{d^2}=\dfrac{ab}{cd}\)

Áp dụng tính chất dãy tỉ số bằng nhau, ta có:

\(\dfrac{a^2}{c^2}=\dfrac{ab}{cd}=\dfrac{7a^2}{7c^2}=\dfrac{3ab}{3cd}=\dfrac{7a^2+3ab}{7c^2+3cd}\)

\(\dfrac{a^2}{c^2}=\dfrac{b^2}{d^2}=\dfrac{11a^2}{11c^2}=\dfrac{8b^2}{8d^2}=\dfrac{11a^2-8b^2}{11c^2-8d^2}\)

⇒\(\dfrac{7a^2+3ab}{7c^2+3cd}=\dfrac{11a^2-8b^2}{11c^2-8d^2}\)

\(\Rightarrow\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\left(đpcm\right)\)