Question

Cho \(\frac{a}{c}=\frac{c}{b}\). CM: \(\frac{a^2+c^2}{b^2+c^2}=\frac{a}{b}\)

Answer 1

\(\Rightarrow\)\(\frac{a}{c}\)=\(\frac{c}{b}\)\(\Rightarrow\) a.b = c.c

\(\Rightarrow\)\(\frac{a^2+c^2}{b^2+c^2}\)=\(\frac{a.a+a.b}{b.b+a.b}\)=\(\frac{a^2}{b^2}\)=\(\frac{a}{b}\)

tíck mình nka

Answer 2

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

\(\Rightarrow ab=c^2\)

\(\Rightarrow ab\left(b-a\right)=c^2\left(b-a\right)\)

\(\Rightarrow ab^2-ba^2=bc^2-ac^2\)

\(\Rightarrow ab^2+ac^2=bc^2+ba^2\)

\(\Rightarrow a\left(b^2+c^2\right)=b\left(a^2+c^2\right)\)

\(\Rightarrow\frac{a}{b}=\frac{a^2+c^2}{b^2+c^2}\)