Question

Giusp mik với mai mik thi r.Please!!

Cho ab=c².CMR:a²+c²/b²+c²=a/b

 

 

 

Answer 1

Thay \(ab=c^2\)vào \(\frac{a^2+c^2}{b^2+c^2}\)ta có

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

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

Answer 2

Cảm ơn bạn nhiều nhiều nha'

Answer 3

Có \(\frac{a}{b}=\frac{b}{c}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\)

Đặt \(\frac{a}{c}=\frac{b}{d}=k\Rightarrow a=c.k;b=d.k\)

\(\Rightarrow a^2=c^2.k^2;b^2=d^2.k^2\)

Khi đó \(\frac{a^2+c^2}{b^2+d^2}=\frac{c^2.k^2+c^2}{d^2.k^2+d^2}=\frac{c^2.\left(k^2+1\right)}{d^2.\left(k^2+1\right)}=\frac{c^2}{d^2}=\frac{a^2}{b^2}\)