Solve-x-2-x-2-2x-

Question Number 15504 by rish@bh last updated on 11/Jun/17

Solve ⌈ x^{2} ⌉ = {(⌊ x ⌋)}^{2} + 2 x

Commented by rish@bh last updated on 11/Jun/17

I got only 0 and . 5 but my book

says \frac{n + 1}{2} and 0

Commented by mrW1 last updated on 11/Jun/17

your book is wrong . you can check

with n = 1 \Rightarrow x = 1 \Rightarrow 1^{2} = 1^{2} + 2!!!

Commented by rish@bh last updated on 11/Jun/17

Thanks!

Answered by mrW1 last updated on 11/Jun/17

2 x = ⌈ x^{2} ⌉ - {(⌊ x ⌋)}^{2} = integer

\Rightarrow x = integer or integer + 0.5

let x = n + f with f = 0 or 0.5

(1) f = 0

x = n

n^{2} = n^{2} + 2 n

\Rightarrow n = 0

\Rightarrow x = 0

(2) f = 0.5

x = n + 0.5

x^{2} = n^{2} + n + 0.25

⌈ x^{2} ⌉ = n^{2} + n + 1

⌊ x ⌋ = n

2 x = 2 n + 1

n^{2} + n + 1 = n^{2} + 2 n + 1

n = 0

\Rightarrow x = 0.5

Facebook Tweet Pin