اگر $\frac{a}{b}=\frac{c}{d}$ باشد، کدام رابطه برقرار است؟ $(m\,\,,\,\,n\in Z\,\,,\,\,\,x\,\,,\,\,y\in R)$
1 )
$\frac{ma+nc}{mb+n{{d}^{2}}}={{\left( \frac{ax}{by} \right)}^{2}}$
2 )
$\frac{ma+nc}{nb+m{{d}^{3}}}=\frac{{{(ax)}^{3}}+{{(cy)}^{3}}}{{{(by)}^{3}}+{{(dx)}^{3}}}$
3 )
$\frac{{{a}^{2}}+{{c}^{2}}}{{{b}^{3}}+{{d}^{3}}}={{\left( \frac{ma+nc}{mb+nd} \right)}^{\frac{2}{3}}}$
${{\left( \frac{ma+nc}{mb+nd} \right)}^{\frac{3}{2}}}=\frac{{{(ax)}^{\frac{3}{2}}}+{{(cy)}^{\frac{3}{2}}}}{{{(bx)}^{\frac{3}{2}}}+{{(dy)}^{\frac{3}{2}}}}$
پاسخ تشریحی :
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