Question

[Phạm Thị Thanh Thanh]

cho a/c=c/b . CMR : a, a/b = ( a^2 + c^2)/(b^2+c^2)

b, ( b-a )/a = ( b^2 - a^2 )/(a^2 + c ^2 )

Answer 1

[Mashiro Shiina]

Đặt:

\(\dfrac{a}{c}=\dfrac{c}{b}=k\Rightarrow\left\{{}\begin{matrix}a=ck\\c=bk\\a=bk^2\end{matrix}\right.\)

\(\dfrac{a}{b}=\dfrac{bk^2}{b}=k^2\)

\(\dfrac{a^2+c^2}{b^2+c^2}=\dfrac{ck^2+bk^2}{b^2+c^2}=\dfrac{k^2\left(c^2+b^2\right)}{b^2+c^2}=k^2\)

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

\(\Rightarrowđpcm\)

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