for positive real number x and y , xy = 16 then find the minimum value of [x]+[y] , [ ] greatest integer function


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Question Number 174211 by infinityaction last updated on 27/Jul/22

$f o r p o s i t i v e r e a l n u m b e r x$ $a n d y, x y = 16 t h e n f i n d t h e$ $m i n i m u m v a l u e o f [x] + [y],$ $[] g r e a t e s t i n t e g e r f u n c t i o n$
	Answered by MJS_new last updated on 27/Jul/22

	$the minimum value is 7 in these intervals :$ $\frac{8}{3} < x < 3 ⌊ x ⌋ = 2 \land ⌊ y ⌋ = 5$ $\frac{16}{5} < x < 4 ⌊ x ⌋ = 3 \land ⌊ y ⌋ = 4$ $4 < x < 5 ⌊ x ⌋ = 4 \land ⌊ y ⌋ = 3$ $\frac{16}{3} < x < 6 ⌊ x ⌋ = 5 \land ⌊ y ⌋ = 2$
	Commented by infinityaction last updated on 27/Jul/22

	$t h a n k s$
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