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If-x-5-x-5-then-x-x-would-be-greater-than-a-5-2-b-5-3-c-5-d-5-1-e-5-1-




Question Number 113154 by I want to learn more last updated on 11/Sep/20
If      ⌊x  +  (√5)⌋   =   ⌊x⌋  +  ⌊5⌋  then     ⌊x⌋  −  x    would be greater than  (a)    (√5)  −  2       (b)    (√5)  −  3      (c)    (√5)        (d)    (√5)  +  1       (e)   (√5)  −  1
$$\mathrm{If}\:\:\:\:\:\:\lfloor\mathrm{x}\:\:+\:\:\sqrt{\mathrm{5}}\rfloor\:\:\:=\:\:\:\lfloor\mathrm{x}\rfloor\:\:+\:\:\lfloor\mathrm{5}\rfloor \\ $$$$\mathrm{then}\:\:\:\:\:\lfloor\mathrm{x}\rfloor\:\:−\:\:\mathrm{x}\:\:\:\:\mathrm{would}\:\mathrm{be}\:\mathrm{greater}\:\mathrm{than} \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:−\:\:\mathrm{2}\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:−\:\:\mathrm{3}\:\:\:\:\:\:\left(\mathrm{c}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\:\:\:\sqrt{\mathrm{5}}\:\:+\:\:\mathrm{1}\:\:\:\:\:\:\:\left(\mathrm{e}\right)\:\:\:\sqrt{\mathrm{5}}\:\:−\:\:\mathrm{1} \\ $$
Answered by 1549442205PVT last updated on 11/Sep/20
[x]−x<0 ,(√5)−2>0,(√5)>0,(√5)+1>0,(√5)−1>0  (√5)−3<0 ,so [x]−x>(√5)−3  Choose b)
$$\left[\mathrm{x}\right]−\mathrm{x}<\mathrm{0}\:,\sqrt{\mathrm{5}}−\mathrm{2}>\mathrm{0},\sqrt{\mathrm{5}}>\mathrm{0},\sqrt{\mathrm{5}}+\mathrm{1}>\mathrm{0},\sqrt{\mathrm{5}}−\mathrm{1}>\mathrm{0} \\ $$$$\sqrt{\mathrm{5}}−\mathrm{3}<\mathrm{0}\:,\mathrm{so}\:\left[\mathrm{x}\right]−\mathrm{x}>\sqrt{\mathrm{5}}−\mathrm{3} \\ $$$$\left.\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{b}}\right) \\ $$
Commented by I want to learn more last updated on 11/Sep/20
Thanks sir
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$

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