Question

Giúp tui zới!!!

Answer 1

Giải:

Đặt \(\dfrac{a}{c}=\dfrac{c}{b}=k\)

\(k^2=\dfrac{a}{c}.\dfrac{c}{b}=\dfrac{a}{b}\) (1)

\(k^2=\dfrac{a^2}{c^2}=\dfrac{c^2}{b^2}=\dfrac{a^2+c^2}{b^2+c^2}\) ( t/c dãy tỉ số bằng nhau )

Từ (1), (2) \(\Rightarrow\dfrac{a^2+c^2}{b^2+c^2}=\dfrac{a}{b}\left(đpcm\right)\)

Answer 2

Ta có \(\dfrac{a}{c}\)= \(\dfrac{c}{b}\) => \(\dfrac{a^2}{c^2}\) = \(\dfrac{c^2}{b^2}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\dfrac{a^2}{c^2}\) = \(\dfrac{c^2}{b^2}\) = \(\dfrac{a^2+c^2}{b^2+c^2}\) (1)

Ta có \(\dfrac{a^2}{c^2}\) = \(\dfrac{a.a}{c.c}\) = \(\dfrac{a.c}{c.b}\)=\(\dfrac{a}{b}\) (vì \(\dfrac{a}{c}\)=\(\dfrac{c}{b}\)) (2)

Từ (1)(2) => \(\dfrac{a^2+c^2}{b^2+c^2}\) = \(\dfrac{a}{b}\) (đpcm)