solve-in-R-2x-3x-1-x-greatest-integer-number-more-than-or-equal-to-x-

Question Number 185981 by mnjuly1970 last updated on 30/Jan/23

s o l v e i n R

⌊ 2 x ⌋ + ⌊ 3 x ⌋ = 1

⌊ x ⌋ := g r e a t e s t i n t e g e r n u m b e r

m o r e t h a n o r e q u a l t o^{″} x^{″}

Answered by mr W last updated on 30/Jan/23

x = n + f

5 n + ⌊ 2 f ⌋ + ⌊ 3 f ⌋ = 1

1 - 5 n = ⌊ 2 f ⌋ + ⌊ 3 f ⌋ ⩾ 0 \Rightarrow n ⩽ 0

1 - 5 n = ⌊ 2 f ⌋ + ⌊ 3 f ⌋ < 5 \Rightarrow n ⩾ 0

\Rightarrow n = 0 \Rightarrow 0 ⩽ x < 1

2 x < 1 \Rightarrow x < \frac{1}{2}

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

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

Commented by mnjuly1970 last updated on 31/Jan/23

m e r c e y s i r W . .