Question

cho a,b,c,d thỏa mãn a/b=c/d CMR:ab/cd=a^2+c^2/b^2+d^2

Answer 1

ta có \(\frac{a}{b}=\frac{c}{d}=>\frac{a}{b}.\frac{d}{c}=1\)

\(\frac{ab}{cd}=\frac{ab}{cd}.1=\frac{ab}{cd}.\frac{a}{b}.\frac{d}{c}=\frac{a^2}{c^2}\)

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

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

áp dụng quy tắc dãy tỉ số bằng nhau\(=>\frac{ab}{cd}=\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a^2+c^2}{b^2+d^2}\)