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Question Number 93953 by mhmd last updated on 16/May/20

	Answered by Rasheed.Sindhi last updated on 16/May/20

	${(x - \frac{1}{x})}^{2} = 5^{2}$ $x^{2} + \frac{1}{x^{2}} - 2 = 25$ $x^{2} + \frac{1}{x^{2}} = 27$ ${(x^{2} + \frac{1}{x^{2}})}^{2} = {(27)}^{2}$ $x^{4} + \frac{1}{x^{4}} = 27^{2} - 2 = 727$ ${(x^{4} + \frac{1}{x^{4}})}^{2} = {(727)}^{2}$ $x^{8} + \frac{1}{x^{8}} = {(727)}^{2} - 2 = 528527$
	Answered by Kunal12588 last updated on 16/May/20

	$x - \frac{1}{x} = 5$ $\Rightarrow x^{2} + \frac{1}{x^{2}} = 25 + 2 = 27$ $\Rightarrow x^{4} + \frac{1}{x^{4}} = 4 / 28 / 49 = 729 - 2 = 727$ $\Rightarrow x^{8} + \frac{1}{x^{8}} = 49 / 28 / 102 / 28 / 49 = 528529 - 2$ $\Rightarrow x^{8} + \frac{1}{x^{8}} = 528527$
	Commented by Rasheed.Sindhi last updated on 16/May/20

	$S i r / M i s s K u n a l!$ $W h a t a r e t h e n u m b e r s ? :$ $4 / 28 / 49$ $49 / 28 / 102 / 28 / 49$
	Commented by Kunal12588 last updated on 17/May/20

	$i w a s s q u a r i n g 27 a n d 727 i n l i n e w i t h o u t$ $c a l c u l a t o r; v e d i c m a t h s$ $f o r a n y 2 - d i g i t n o .$ $s u p p o s e A B$ ${(A B)}^{2} = A^{2} / 2 \times A \times B / B^{2}$ $e v e r y / / s l o t s g i v e o n l y o n e s i n g l e d i g i t$ $e g . 34^{2} = 9 / 2 \times 3 \times 4 / 16$ $= 9 / 24 / 16$ $s i n c e w e h a v e 2 - d i g i t i n r i g h t s l o t$ $w e c a n c a r r y o v e r t h e e x t r a d i g i t$ $= 9 / 24 + 1 / 6$ $= 9 / 25 / 6$ $= 9 + 2 / 5 / 6$ $= 11 / 5 / 6$ $= 1156 a n s w e r$ $w i t h p r a c t i c e w e c a n d o i t i n s i n g l e l i n e$ $a n d m u c h f a s t e r; h e r e t h e y {d o n}^{'} t a l l o w$ $c a l c u l a t o r i n s c h o o l s o w e l e a r n s o m e t r i c k s .$ ${(A B C)}^{2} = A^{2} / 2 \cdot A \cdot B / B^{2} + 2 \cdot A \cdot C / 2 \cdot B \cdot C / C^{2}$ $B T W, I a m M a l e, K u n a l i s n o r m a l I n d i a n$ $m a l e n a m e .$
	Commented by Rasheed.Sindhi last updated on 19/Jun/20

	$T h a n k y o u K u n a l s i r f o r d e t a i l e d$ $c l e a r & e a s y t o u n d e r s t a n d$ $a n s w e r . I t h i n k y o u m a y b e a g o o d$ $t e a c h e r . S o m e t i m e a g o I h a d g o t$ $a s m a l l b o o k : V e d i c m a t h e m a t i c s .$ $I l i k e d i t v e r y m u c h b u t i t i s m a t t e r$ $o f s o r r o w t h a t I {c o u l d n}^{'} t b e^{'} u s e d - {t o}^{'}$ $o f t h e t r i c k s o f b o o k!$ $S o r r y f o r w r i t i n g^{'} {m i s s}^{'} f o r y o u$
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