solve-in-R-1-x-x-2-

Question Number 190625 by mnjuly1970 last updated on 07/Apr/23

solve in R :

⌊ \frac{1}{x} ⌋ + ⌊ x ⌋ = 2

Answered by mr W last updated on 07/Apr/23

i f x > 1 :

⌊ \frac{1}{x} ⌋ = 0

\Rightarrow ⌊ x ⌋ = 2

\Rightarrow 2 ⩽ x < 3 ✓

i f x = 1 :

1 + 1 = 2 ✓

i f x < 1 :

⌊ x ⌋ = 0

\Rightarrow ⌊ \frac{1}{x} ⌋ = 2

\Rightarrow 2 ⩽ \frac{1}{x} < 3

\Rightarrow \frac{1}{3} < x ⩽ \frac{1}{2} ✓

s u m m a r y :

\frac{1}{3} < x ⩽ \frac{1}{2}, x = 1, 2 ⩽ x < 3

Commented by mnjuly1970 last updated on 07/Apr/23

t h a n k y o u s o m u c h s i r W \dots