Question

Please solve this question​

Answer 1

Step-by-step explanation:

$\frac{x}{a} = \frac{y}{b} = \frac{z}{c} = k \\ = > \frac{x}{a} = k \\ = > x = ak \\ \frac{y}{b} = k \\ = > y = kb \\ = > \frac{z}{c} = k \\ = > z = kc \\ \\ put \: value \: of \: x \: y \: and \: z \: in \: equation \\ \\ { \frac{ {a}^{2} {x}^{2} + {b}^{2} {y}^{2} + {c}^{2} {z}^{2} }{ {a}^{3} x + {b}^{3}y + {c}^{3}z } }^{ \frac{3}{2} } \\ { \frac{ {a}^{2} {ka}^{2} + {b}^{2} {kb}^{2} + {c}^{2} {kc}^{2} }{ {a}^{3}(ka) + {b}^{3}(kb) + {c}^{3}(kc } }^{ \frac{3}{2} } \\ = > { \frac{ {k}^{2}( {a}^{4} + {b}^{4} + {c}^{4} }{k( {a}^{4} + {b}^{4} + {c}^{4} )} }^{ \frac{3}{2} } \\ = > { \frac{ {k}^{2} }{k} }^{ \frac{3}{2} } \\ = > { k }^{ \frac{3}{2} } \\ = > { {k}^{ 3 } }^{ \frac{1}{2} } \\ = > {k \times k \times k}^{ \frac{1}{2} } \\ = > from \: above \: put \: value \: of \: k \: one \: by \: one \\ = > { \frac{x}{a} \times \frac{y}{b} \times \frac{z}{c} }^{ \frac{1}{2} } \\ = > \sqrt{ \frac{xyz}{abc} }$