how-many-integer-solutions-are-there-1-2-x-3-

Question Number 155144 by mnjuly1970 last updated on 26/Sep/21

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

a r e t h e r e :

⌊ \frac{1}{2 + \sqrt{x}} ⌋ = 3

Commented by mr W last updated on 26/Sep/21

n o i n t e g e r s o l u t i o n a n d e v e n

n o r e a l s o l u t i o n!

s i n c e x ⩾ 0 \Rightarrow 2 + \sqrt{x} ⩾ 2

\Rightarrow 0 < \frac{1}{2 + \sqrt{x}} ⩽ \frac{1}{2}

\Rightarrow ⌊ \frac{1}{2 + \sqrt{x}} ⌋ = 0 \neq 3

Commented by mnjuly1970 last updated on 26/Sep/21

g r a t e f u l \dots m r W

Commented by talminator2856791 last updated on 26/Sep/21

is the question supposed to be

⌊ \frac{1}{2 - \sqrt{x}} ⌋ = 3

?