Question

chung minh rang 7a^2 + 3ab / 11a^2 -8b^2 = 7c^2 + 3cd / 11c^2 - 8d^2

 

 

Answer 1

Đề bài : Cho \(\frac{a}{c}=\frac{b}{d}.CMR:...\)

Ta có : 

\(\frac{a}{c}=\frac{b}{d}\)

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

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

ADTCDTSBN , ta có : 

\(\frac{7a^2}{7c^2}=\frac{3ab}{3cd}=\frac{7a^2+3ab}{7c^2+3cd}\left(1\right)\)

\(\frac{11a^2}{11c^2}=\frac{8b^2}{8d^2}=\frac{11a^2-8b^2}{11c^2-8d^2}\left(2\right)\)

Từ ( 1 ) ; ( 2 ) 

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

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