Question

Cho \(\frac{a}{c}=\frac{c}{b}\)chứng minh rằng:

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

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

Answer 1

a) \(\frac{a}{c}=\frac{c}{b}\)

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

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

\(\frac{b^2-a^2}{a^2+c^2}=\frac{b^2-ab+ab-a^2}{a^2+ab}=\frac{\left(b-a\right)b+\left(b-a\right)a}{a.\left(a+b\right)}=\frac{\left(b-a\right)\left(b+a\right)}{a.\left(a+b\right)}=\frac{b-a}{a}\)

Answer 2

cho mk hỏi viết phan số bằng cách nào vậy