solve-for-all-x-x-2-x-2-100-

Question Number 174960 by alcohol last updated on 14/Aug/22

s o l v e f o r a l l x

⌊ x^{2} ⌋ - ⌊ x ⌋^{2} = 100

Answered by mr W last updated on 15/Aug/22

s a y x = n + f w i t h 0 ⩽ f < 1

⌊ n^{2} + 2 n f + f^{2} ⌋ - n^{2} = 100

⌊ 2 n f + f^{2} ⌋ = 100

100 = ⌊ 2 n f + f^{2} ⌋ < 2 n + 1

\Rightarrow n > 49.5 \Rightarrow n ⩾ 50

⌊ x^{2} ⌋ = 100 + n^{2}

100 + n^{2} ⩽ x^{2} < 101 + n^{2}

\Rightarrow \sqrt{100 + n^{2}} ⩽ x < \sqrt{101 + n^{2}} w i t h n ⩾ 50

Commented by alcohol last updated on 15/Aug/22

t h a n k y o u

p l e a s e c a n y o u e x p l a i n ?

Commented by mr W last updated on 15/Aug/22

i t h o u g h t i h a v e g i v e n a l l n e c e s s a r y

s t e p s .

w h e r e d o y o u n e e d m o r e e x p l a n a t i o n ?

Commented by alcohol last updated on 15/Aug/22

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

t o r e a d i w i l l b e g r a t e f u l

Commented by mr W last updated on 15/Aug/22

s i n c e y o u a s k e d t h i s q u e s t i o n, i a s s u m e d

t h a t y o u k n o w w h a t t h e g r e a t e s t i n t e g e r

f u n c t i o n ⌊ x ⌋ i s . i {d o n}^{'} t k n o w a n y b o o k s

a b o u t s u c h t h i n g s .

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