Question-61537

Question Number 61537 by aanur last updated on 04/Jun/19

Commented by aanur last updated on 04/Jun/19

s i r c o u l d y o u h e l p m e

Commented by math1967 last updated on 04/Jun/19

x y z \times \sqrt{x^{2} \times y^{2} \times z^{2}} = 4 \times 9 \times 16

x^{2} \times y^{2} \times z^{2} = 4 \times 9 \times 16 \Rightarrow x y z = 2 \times 3 \times 4

Answered by MJS last updated on 04/Jun/19

(1) \Rightarrow z = \frac{16}{x^{2} y}

(2) \frac{4 \sqrt{y}}{\sqrt{x}} = 9

(3) \frac{16}{\sqrt{x^{3} y}} = 16

(2) \Rightarrow y = \frac{81 x}{16} \Rightarrow z = \frac{256}{81 x^{3}}

(3) \frac{64}{9 x^{2}} = 16 \Rightarrow x = \frac{2}{3} \Rightarrow y = \frac{27}{8} \land z = \frac{32}{3}

Answered by Kunal12588 last updated on 04/Jun/19

i) x \sqrt{y z} = 4

i i) y \sqrt{x z} = 9

i i i) z \sqrt{x y} = 16

i \times i i \times i i i

\Rightarrow x y z \sqrt{x^{2} y^{2} z^{2}} = 2^{6} \times 3^{2}

\Rightarrow {(x y z)}^{2} = 2^{6} \times 3^{2}

\Rightarrow x y z = 2^{3} \times 3 = 24

{(i)}^{2}

\Rightarrow x^{2} y z = 4^{2} = 16

\Rightarrow \frac{x^{2} y z}{x y z} = \frac{16}{24}

\Rightarrow x = \frac{2}{3}

{(i i)}^{2}

\Rightarrow {x y}^{2} z = 81

\Rightarrow y = \frac{81}{24} = \frac{27}{8}

{(i i i)}^{2}

\Rightarrow {x y z}^{2} = 256

\Rightarrow z = \frac{256}{24} = \frac{32}{3}