Given-x-y-and-x-2-25x-y-y-2-x-25y-solve-for-the-value-of-x-2-y-2-1-without-using-calculators-or-tools-Show-your-method-

Question Number 138193 by mey3nipaba last updated on 10/Apr/21

G i v e n x \neq y a n d x^{2} = 25 x + y, y^{2} = x + 25 y

s o l v e f o r t h e v a l u e o f \sqrt{x^{2} + y^{2} + 1} w i t h o u t

u s i n g c a l c u l a t o r s o r t o o l s .

S h o w y o u r m e t h o d .

Answered by liberty last updated on 11/Apr/21

x^{2} = 25 x + y

y^{2} = x + 25 y

\Rightarrow x^{2} + y^{2} = 26 (x + y)

\Rightarrow x^{2} - y^{2} = 24 (x - y)

\Rightarrow (x - y) [(x + y) - 24] = 0

\Rightarrow x + y = 24

\sqrt{x^{2} + y^{2} + 1} = \sqrt{26.24 + 1}

= \sqrt{(25 + 1) (25 - 1) + 1}

= \sqrt{25^{2}} = 25

Commented by mey3nipaba last updated on 11/Apr/21

t h a n k y o u v e r y m u c h . I a p p r e c i a t e .

Commented by mey3nipaba last updated on 11/Apr/21

B u t p l e a s e I d o n o t u n d e r s t a n d f r o m w h e r e

y o u e q u a t e d i t t o 0 . C a n y o u e x p l a i n ?

Commented by liberty last updated on 11/Apr/21

\Rightarrow x^{2} - y^{2} - 24 (x - y) = 0

\Rightarrow (x - y) (x + y) - 24 (x - y) = 0

\Rightarrow (x - y) (x + y - 24) = 0

s i n c e x \neq y i t f o l l o w s t h a t x + y - 24 = 0

Commented by mey3nipaba last updated on 11/Apr/21

T h a n k s . I g e t t h i s n o w b u t t h e p a r t w h e r e

y o u h a d 26.4 a s t h e v a l u e o f x^{2} + y^{2} .

{I s n}^{'} t i t s u p p o s e d t o b e 264 ?