Question

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

biết rằng \(\frac{a}{b}=\frac{c}{d}\)

Answer 1

Bạn vào câu hỏi tương tự nhé !!!

Answer 2

hai cái đấy giống hệt nhau 

Answer 3

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

mặt khác,ta có:

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

vậy nếu a/b=c/d thì 7a^2+3ab/7c^2+3cd/11a^2-8b^2/11c^2-8d^2(đpcm)

tick nhé