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# Greatest integer function

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Find x such that

$$​​​​​​\lfloor x \rfloor \cdot x = 70$$

express x as a decimal.

Jun 19, 2018
edited by cormier123  Jun 19, 2018
edited by cormier123  Jun 19, 2018

#1
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HEY CORMIER(123)! i'll be glad to answer. assuming that those weird bracket thingy mean absolulet valuve, you can assume that x has to be positive. then, that means (x)^2=70, which acordding to my caculator, its bout 8.36. HOPE THIS HELPED!

Jun 19, 2018
#2
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PS, tell me if im wrong, and if it's AoPS, paste answer herre. -LUNAMORT 4 LIFE or Purely Slytherin

Jun 19, 2018
#3
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Hi, $$​​​​​​\lfloor x \rfloor$$ that doesn't represent aboslute value, it denotes the greatest integer that is less than or equal to x, otherwise called the "Greatest integer function."

cormier123  Jun 19, 2018
#4
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I don't know the correct way to solve this, but first I guessed that x is 8 point something,

which makes  floor(x) = 8

And   70 / 8  =  8.75    , so this works:       $$​​​​​​\lfloor 8.75 \rfloor \cdot 8.75 = 70$$

Jun 20, 2018
#5
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cormier is right. the weird absolute value thing is NOT absolute value, it represents the greatest integer less than or equal to x. so yeah, thus x would be 8.75

Jun 20, 2018
edited by kevbamboo  Jun 20, 2018