x-1-x-5-and-x-y-4-find-x-2-1-y-2-

Question Number 191451 by mathlove last updated on 24/Apr/23

x + \frac{1}{x} = 5 a n d x \cdot y = 4 f i n d

x^{2} + {(\frac{1}{y})}^{2} = ?

Answered by mr W last updated on 24/Apr/23

x^{2} - 5 x + 1 = 0

x = \frac{5 \pm \sqrt{21}}{2}

x^{2} = 5 x - 1

{(\frac{1}{y})}^{2} = {(\frac{x}{4})}^{2} = \frac{x^{2}}{16}

x^{2} + {(\frac{1}{y})}^{2} = \frac{17 x^{2}}{16} = \frac{17}{16} (5 x - 1)

= \frac{17}{16} (5 \times \frac{5 \pm \sqrt{21}}{2} - 1) = \frac{391 \pm 85 \sqrt{21}}{32}

Commented by mehdee42 last updated on 24/Apr/23

s i r W

p l e a s e g u i d e m e h o w c a n i s u b m i t a q u e s t i o n i n t h e g r o u p ?

Commented by Tinku Tara last updated on 24/Apr/23

Just press + button at top .

Commented by mr W last updated on 24/Apr/23

t o c o m p o s e a n e w q u e s t i o n j u s t p r e s s

“ +^{″} b u t t o n a t t h e t o p;

t o p o s t a n i m a g e a s a q u e s t i o n j u s t

p r e s s “ {i m a g e}^{″} b u t t o n a t t h e t o p .

Commented by mr W last updated on 24/Apr/23

Commented by mehdee42 last updated on 24/Apr/23

t h a n k y o u v e r y m u c h f o r y o u r k i d n e s s

Commented by mathlove last updated on 25/Apr/23

t h a n k s