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21 Jul 2013, 07:51
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[x] denotes the greatest integer value just below x and {x} its fractional value.The sum of
[x]^3 and {x}^2 is -7.91.Find x.
a)-2.03
b)-1.97
c)-2.97
d)-1.7
Please provide the solution with explanation.
[x]^3 and {x}^2 is -7.91.Find x.
a)-2.03
b)-1.97
c)-2.97
d)-1.7
Please provide the solution with explanation.
21 Jul 2013, 22:12
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SAMHITAC
What does this statement mean? "[x] denotes the greatest integer value just below x and {x} its fractional value."
It means x = [x] (integer part) + {x} (fractional part)
Say if x = 2.34, [x] = 2 (integer part) and {x} = .34 (fractional part)
Say if x = -2.34, [x] = -3 (note that -3 is the integer smaller than -2.34, not -2) and {x} = .66 because -3 + .66 = -2.34
etc
[x]^3 + {x}^2 = -7.91
[x]^3 must be negative to get -7.91 so [x] must be negative. {x}^2 will be positive and fractional (less than 1) since {x} is less than 1.
[x]^3 must be -8 so [x] must be -2.
So {x}^2 = (-7.91) - (-8) = .09
This means {x} = 0.3
x = [x] + {x} = -2 + .3 = -1.7
