Toán Cho x/a = y/b = z/c Cmr: a^2/x + b^2/y +c^2/z =(a+b+c)/x+y+z 20/07/2021 By Maya Cho x/a = y/b = z/c Cmr: a^2/x + b^2/y +c^2/z =(a+b+c)/x+y+z
Giải thích các bước giải: $\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}=k$ $\rightarrow \begin{cases}x=ak\\y=bk\\z=ck\end{cases}$ $\rightarrow\dfrac{a^2}{x}+\dfrac{b^2}{y}+\dfrac{c^2}{z}=\dfrac{a^2}{ak}+\dfrac{b^2}{bk}+\dfrac{c^2}{ck}=\dfrac{a+b+c}{k}$ Mà $\dfrac{a+b+c}{x+y+z}=\dfrac{a+b+c}{ka+kb+kc}=\dfrac{a+b+c}{k(a+b+c)}=\dfrac{1}{k}$ $\rightarrow \dfrac{a^2}{x}+\dfrac{b^2}{y}+\dfrac{c^2}{z}\ne\dfrac{a+b+c}{x+y+z} $ Trả lời
Giải thích các bước giải:
$\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}=k$
$\rightarrow \begin{cases}x=ak\\y=bk\\z=ck\end{cases}$
$\rightarrow\dfrac{a^2}{x}+\dfrac{b^2}{y}+\dfrac{c^2}{z}=\dfrac{a^2}{ak}+\dfrac{b^2}{bk}+\dfrac{c^2}{ck}=\dfrac{a+b+c}{k}$
Mà $\dfrac{a+b+c}{x+y+z}=\dfrac{a+b+c}{ka+kb+kc}=\dfrac{a+b+c}{k(a+b+c)}=\dfrac{1}{k}$
$\rightarrow \dfrac{a^2}{x}+\dfrac{b^2}{y}+\dfrac{c^2}{z}\ne\dfrac{a+b+c}{x+y+z} $