Question

CMR: \(\dfrac{a}{b}=\dfrac{b}{c}thi\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a}{c}\left(b,c\ne0\right)\)

mọi người cứu em vs mai em thi học kì rùi huhu

Answer 1

Ap dung tnh chat day ti so bang nhau ta co:

a/b=b/c suy ra a^2/b^2=b^2/c^2=(a^2+b^2)/(b^2+c^2)

suy ra a^2/b^2=(a^2+b^2)/(b^2+c^2)

suy ra a/b.b/c=(a^2+b^2)/(b^2+c^2)

suy ra a/c= (a^2+b^2)/(b^2+c^2)

Answer 2

Vì \(\dfrac{a}{b}=\dfrac{b}{c}\) \(=>ac=b^2\)

Ta có: \(\dfrac{a^2+b^2}{b^2+c^2}=\dfrac{a^2+ac}{ac+c^2}=\dfrac{a.\left(a+c\right)}{c.\left(a+c\right)}=\dfrac{a}{c}\)(đpcm)