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Question Number 190972 by pascal889 last updated on 15/Apr/23

	Answered by Frix last updated on 15/Apr/23

	$\frac{1}{2 - \sqrt{3}} = 2 + \sqrt{3} \land \frac{1}{2 + \sqrt{3}} = 2 - \sqrt{3}$ $a = 2 \land b = \sqrt{3}$ ${(a + b)}^{2} + {(a - b)}^{2} = 2 (a^{2} + b^{2}) = 14$
	Answered by Rasheed.Sindhi last updated on 15/Apr/23

	$AnOther way$ $m = \frac{1}{2 - \sqrt{3}} = 2 + \sqrt{3}$ $n = \frac{1}{2 + \sqrt{3}} = 2 - \sqrt{3}$ $m^{2} + n^{2} = {(m + n)}^{2} - 2 m n$ $= {(2 + \sqrt{3} + 2 - \sqrt{3})}^{2} - 2 (2 + \sqrt{3}) (2 - \sqrt{3})$ ${(4)}^{2} - 2 (4 - 3) = 16 - 2 = 14$
	Commented by Acem last updated on 16/Apr/23

	$N i c e m o n a m i R a s h e e d$ $S o l o n g i {d i d n}^{'} t c o m e$ $H o p e y o u a n d a l l a r e o k e y$
	Commented by Rasheed.Sindhi last updated on 16/Apr/23

	$W e l c o m e s i r A c e m!$ $M i s s e d y o u a l o t, d u r i n g y o u r$ $l o n g t e r m a b s e n c e . . .$ $I r e m e m b e r y o u r e x c i t i n g c o m m e n t s . . .$ $B T W,$ $w h e r e w e r e y o u i n t h i s p e r i o d s i r ?$
	Commented by Acem last updated on 17/Apr/23

	$I m i s s e d y o u t o o, a m g l a d t h a t y o u a n d a l l$ $a r e o k e y w i t h a l l m y h e a r t!$ $M y c o u n t r y i s s t i l l i n a w a r, i l o s t a l l m y$ $b o o k s, p l a n s a n d m y o w n s t u d i e s f i v e y e a r s$ $a g o . U n t i l l n o w i {h a v e n}^{'} t b e e n a b l e t o s e t t l e$ $i n a s a f e p l a c e .$ $O n e d a y, i w i l l r e s t o r e a l l m y k n o w l e d g e .$ $L i f e i s c r u e l a n d m y s o u l k n o w s$ $n o d e s p a i r .$
	Commented by manxsol last updated on 17/Apr/23

	$B i e n v e n i d o, S i r A c e m, 104$ $d i a s s i n s u s a b i d u r i a y s u s$ $b u e n o s c o n s e j o s . Q u e t o d o$ $m e j o r e p a r a U s t e d .$
	Commented by Rasheed.Sindhi last updated on 17/Apr/23

	$@ A c e m$ $V e r y s a d t o h e a r a b o u t y o u r$ $c i r c u m s t a n c e s . . . b t w w h i c h c o u n t r y$ $d o y o u b e l o n g t o ? . . . W e l l w i s h e s$ $a b o u t y o u r f u t u r e s i r!$
	Commented by Acem last updated on 22/Apr/23

	$@ M r . M a n x s o l B i e n v e n i d o :) C o m o e s t a ?$ $E s p e r o q u e e s t e s b i e n .$ $P i d o d i s c u l p a s p o r e s t a a u s e n c i a i n v o l u n t a r i a .$ $E s p e r a m o s d i a s m e j o r e s .$ $L a c i e n c i a q u e s i r v e a l a h u m a n i d a d e s d e b i l e$ $i m p o t e n t e a n t e l a c i e n c i a p r i v a d a$ $q u e s i r v e a l o s d e m o n i o s i n m o r a l e s d e l m u n d o$ $S o m o s l a s u n i c a s v i c t i m a s, y n a d a m a s p a r a$ $b l a n q u e a r e l r o s t r o d e l a c i v i l i z a c i o n$
	Commented by Acem last updated on 22/Apr/23

	$@ S i r R a s h e e d, t h a n k y o u s o m u s h :)$ $f o r y o u r w i s h e s i n e e d .$ $S y r i a$
	Commented by Rasheed.Sindhi last updated on 22/Apr/23

	$T h a n k s s i r A c e m!$ $M a y G o d p r o t e c t y o u a n d y o u r$ $c o u n t r y f r o m w a r!$
	Commented by Acem last updated on 23/Apr/23

	$B i g t h a n k s s i r R a s h e e d!$ $M a y A l l a h b l e s s y o u,$ $A m i n f o r a l l$
	Commented by Rasheed.Sindhi last updated on 25/Apr/23
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	Answered by manxsol last updated on 16/Apr/23

	$m + n = 4 m n = 1$ $m^{2} + n^{2} = {(4)}^{2} - 2 = 14$
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