If-xy-1-3-xz-3-8-and-yz-1-2-For-x-y-and-z-compare-

Question Number 207197 by hardmath last updated on 09/May/24

If xy = \frac{1}{3}, xz = \frac{3}{8} and yz = \frac{1}{2}

For x, y and z compare .

Answered by A5T last updated on 09/May/24

x = \frac{1}{3 y}; z = \frac{1}{2 y}

x z = \frac{3}{8} \Rightarrow \frac{1}{6 y^{2}} = \frac{3}{8} \Rightarrow y^{2} = \frac{4}{9} \Rightarrow y = \underline{+} \frac{2}{3}

\Rightarrow x = \underline{+} \frac{1}{2}; z = \underline{+} \frac{3}{4}

Answered by mr W last updated on 09/May/24

(i) \times (i i) \times (i i i) :

{(x y z)}^{2} = \frac{1}{3} \times \frac{3}{8} \times \frac{1}{2} = \frac{1}{16}

\Rightarrow x y z = \pm \frac{1}{4} \dots (i v)

(i v) / (i) :

z = \pm \frac{3}{4}

(i v) / (i i) :

y = \pm \frac{2}{3}

(i v) / (i i i) :

x = \pm \frac{1}{2}

Commented by hardmath last updated on 09/May/24

dear professor, x, y, z > 0

Commented by mr W last updated on 09/May/24

b u t i t w a s n o t s a i d t h a t x, y, z > 0 .

Commented by mr W last updated on 09/May/24

i f x, y, z > 0 t h e n x < y < z

Commented by hardmath last updated on 09/May/24

thank you dear professor