Question

已知a/b=c/d求证a/b=（a^2+c^2）/（ab+cd）

Answer 1

设A/B=C/D=K

则A=KB C=KD

(A^2+C^2)/(AB+CD)

=(K^2*B^2+K^2*D^2)/(K*B^2+K*D^2)

=[K^2(B^2+D^2)]/[K(B^2+D^2)]

=K

=A/B