Question

cho \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng minh rằng

với \(b^2\)=ac thì \(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\)

Answer 1

Xét \(\left(a^2+b^2\right).C-\left(b^2+c^2\right).a=a^2c+b^2a\)=\(b^2a-c^2a=a^2c+ac.c-ac.a=0\)

(thay \(b^2=ac\))

\(\Rightarrow\left(a^2+b^2\right).c=\left(b^2+c^2\right).a\Rightarrow\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\)

Answer 2

ý lộn r