for-positive-real-number-x-and-y-xy-16-then-find-the-minimum-value-of-x-y-greatest-integer-function-

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

$${for}\:{positive}\:{real}\:{number}\:{x}\: \\ $$$${and}\:{y}\:,\:{xy}\:=\:\mathrm{16}\:{then}\:{find}\:{the} \\ $$$$\:{minimum}\:{value}\:{of}\:\:\left[{x}\right]+\left[{y}\right]\:, \\ $$$$\left[\:\right]\:{greatest}\:{integer}\:{function} \\ $$

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

$${thanks} \\ $$

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