Question

Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) . Chứng minh :

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

Answer 1

Ta có:

\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}\Rightarrow\dfrac{a^2}{c^2}=\dfrac{b^2}{d^2}\Rightarrow\dfrac{a.b}{c.d}\)

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

\(\dfrac{a^2}{c^2}=\dfrac{b^2}{d^2}=\dfrac{a.b}{c.d}\)

\(\Rightarrow\dfrac{7a^2}{7c^2}=\dfrac{11a^2}{11c^2}=\dfrac{8b^2}{8d^2}=\dfrac{3a.b}{3c.d}\)

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

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

\(\Rightarrow\left(đpcm\right)\)