Question

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

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

Answer 1

Đặt: \(\dfrac{a}{b}=\dfrac{c}{d}=t\Leftrightarrow\left\{{}\begin{matrix}a=bt\\c=dt\end{matrix}\right.\)

Ta có: \(\left\{{}\begin{matrix}\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7b^2t^2+3b^2t}{11b^2t^2-8b^2}=\dfrac{b^2\left(7t^2+3t\right)}{b^2\left(11t^2-8\right)}=\dfrac{7t^2+3t}{11t^2-8}\\\dfrac{7c^2+3cd}{11c^2-8d^2}=\dfrac{7d^2t^2+3d^2t}{11d^2t^2-8d^2}=\dfrac{d^2\left(7t^2+3t\right)}{d^2\left(11t^2-8\right)}=\dfrac{7t^2+3t}{11t^2-8}\end{matrix}\right.\Rightarrowđpcm\)