Question Number 174211 by infinityaction last updated on 27/Jul/22
![for positive real number x and y , xy = 16 then find the minimum value of [x]+[y] , [ ] greatest integer function](Q174211.png)
$${for}\:{positive}\:{real}\:{number}\:{x}\: \\ $$$${and}\:{y}\:,\:{xy}\:=\:\mathrm{16}\:{then}\:{find}\:{the} \\ $$$$\:{minimum}\:{value}\:{of}\:\:\left[{x}\right]+\left[{y}\right]\:, \\ $$$$\left[\:\right]\:{greatest}\:{integer}\:{function} \\ $$
Answered by MJS_new last updated on 27/Jul/22
$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{is}\:\mathrm{7}\:\mathrm{in}\:\mathrm{these}\:\mathrm{intervals}: \\ $$$$\frac{\mathrm{8}}{\mathrm{3}}<{x}<\mathrm{3}\:\:\:\:\:\lfloor{x}\rfloor=\mathrm{2}\wedge\lfloor{y}\rfloor=\mathrm{5} \\ $$$$\frac{\mathrm{16}}{\mathrm{5}}<{x}<\mathrm{4}\:\:\:\:\:\lfloor{x}\rfloor=\mathrm{3}\wedge\lfloor{y}\rfloor=\mathrm{4} \\ $$$$\mathrm{4}<{x}<\mathrm{5}\:\:\:\:\:\lfloor{x}\rfloor=\mathrm{4}\wedge\lfloor{y}\rfloor=\mathrm{3} \\ $$$$\frac{\mathrm{16}}{\mathrm{3}}<{x}<\mathrm{6}\:\:\:\:\:\:\lfloor{x}\rfloor=\mathrm{5}\wedge\lfloor{y}\rfloor=\mathrm{2} \\ $$
Commented by infinityaction last updated on 27/Jul/22
$${thanks} \\ $$