The number of solutions of the equation x = 2{x}, where {x} is the fractional part of x, is
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The number of solutions of the equation x = 2{x}, where {x} is the fractional part of x, is
The number of solutions of the equation x = 2{x}, where {x} is the fractional part of x, is
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Given : x = 2{x}, where {x} is the fractional part of x
To Find : number of solutions of the equation x = 2{x}
Solution:
{x} is the fractional part of x
=> {x} = x - [ x ]
[ x ] represent greatest integer function
x = 2{x}
=> x = 2 ( x - [ x ] )
=> x = 2x - 2 [ x ]
=> x = 2 [ x ]
[ x ] is integer => 2 [ x ] must be an integer
Hence x must be integer
Integer x = 2x
=> x = 0
Hence x = 0 is the only solution
x = 2{x}
number of solutions of the equation x = 2{x} is 1
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