Question

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

Giups mk với các bn ơi

Answer 1

Ta có : a/b=b/c

suy ra ac= b^2 thay vào ta có

a^2+ ac/ ac+c^2 = a(a+c)/ c(a+c) = a/c

vậy a^2+b^2/ b^2 + c^2 = a/c

Answer 2

\(từ\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)

Đặt \(\frac{a}{c}=\frac{b}{d}=k\Rightarrow a=ck,b=dk\)

\(\Rightarrow\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}=\frac{ck+c}{dk+d}=\frac{c^2k^2+c^2}{d^2k^2+d^2}=\frac{c^2\left(k^2+1\right)}{d^2\left(k^2+1\right)}=\frac{c^2}{d^2}=\frac{a^2}{b^2}=\frac{a}{c}\)(đpcm)

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