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Ta có: \(\frac{a}{k}=\frac{x}{a};\frac{b}{k}=\frac{y}{b}\)
=> a2 = x.k; b2 = y.k
=> \(\frac{a^2}{b^2}=\frac{x.k}{y.k}=\frac{x}{y}\left(đpcm\right)\)
a/k = x/a => a2 = kx (1)
b/k = y/b => b2 = ky (2)
chia (1) cho (2) có;
a2/b2 =x/y
ta có
\(\frac{a}{k}=\frac{x}{a}=>a^2=kx\left(1\right)\)
\(\frac{b}{k}=\frac{y}{b}=>b^2=ky\left(2\right)\)
từ (1)và (2) , ta có
\(\frac{a^2}{b^2}=\frac{kx}{ky}=\frac{x}{y}\)
vậy \(\frac{a^2}{b^2}=\frac{x}{y}\)
\(\frac{a^2}{b^2}=\frac{kx}{ky}=\frac{x}{y}\)
Ta có: \(\frac{a}{k}=\frac{x}{a}=>a^2=k\cdot x\)
\(\frac{b}{k}=\frac{y}{b}=>b^2=k\cdot y\)
=> \(\frac{a^2}{b^2}=\frac{kx}{ky}=\frac{x}{y}\)(rút gọn)
=>đpcm
Chúc bạn học tốt!^_^
Ta có :
\(\begin{cases}\frac{a}{k}=\frac{x}{a}\\\frac{b}{k}=\frac{y}{b}\end{cases}\)
\(\Rightarrow\begin{cases}a^2=kx\\b^2=ky\end{cases}\)
Chia về theo vế
\(\Rightarrow a^2:b^2=\left(kx\right):ky\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{kx}{ky}\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{x}{y}\)
Có: \(\left\{{}\begin{matrix}\frac{a}{k}=\frac{x}{a}\\\frac{b}{k}=\frac{y}{b}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a^2=kx\\b^2=ky\end{matrix}\right.\\ \Rightarrow\frac{a^2}{b^2}=\frac{kx}{ky}=\frac{x}{y}\)
Ta có:
\(\left\{{}\begin{matrix}\frac{a}{k}=\frac{x}{a}\Rightarrow a^2=kx\\\frac{b}{k}=\frac{y}{b}\Rightarrow b^2=ky\end{matrix}\right.\)
Chia theo vế ta được:
\(a^2:b^2=kx:ky\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{kx}{ky}\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{x}{y}\left(đpcm\right).\)
Chúc bạn học tốt!
Ta có
\(\frac{a}{k}=\frac{x}{a}<=>a^2=x.k\)
\(\frac{b}{k}=\frac{y}{b}<=>b^2=k.y\)
=>\(\frac{a^2}{b^2}=\frac{x.k}{k.y}=\frac{x}{y}\)
tick nha
\(\frac{a}{k}=\frac{x}{a}\Leftrightarrow a^2=kx\)
\(\frac{b}{k}=\frac{y}{b}\Leftrightarrow b^2=ky\)
\(\frac{a^2}{b^2}=\frac{kx}{ky}=\frac{x}{y}\)
\(\frac{k}{x}=\frac{a}{c}\Rightarrow kc=ax;\frac{k}{y}=\frac{b}{d}\Rightarrow kd=by\)
ax+by=kc+kd=k(c+d)=k.k=k2
=>đpcm
\(\frac{a}{k}=\frac{x}{a}\Rightarrow a^2=xk;\frac{b}{k}=\frac{y}{b}\Rightarrow b^2=ky\)
=>\(\frac{a^2}{b^2}=\frac{xk}{yk}=\frac{x}{y}\)
\(\frac{a}{k}=\frac{x}{a}\Rightarrow a^2=k.x\)
\(\frac{b}{k}=\frac{y}{b}\Rightarrow b^2=y.k\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{k.x}{y.k}=\frac{x}{y}\Rightarrow\frac{a^2}{b^2}=\frac{x}{y}\left(đpcm\right)\)