The difference of cube and square of a real number is equal to the difference of its square and it

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05 Feb 2010 Square and Cube

The difference of cube and square of a real number is equal to the difference of its square and itself.
Total number of such real numbers are

OPtion

(1) 2
(2) 0
(3) 1
(4) 3
(5) 4

Solution

Let the number is x, then according to given condition

x^3 - x^2 = x^2 - x

x^3 - 2x^2 + x = 0
x ( x^2 – 2x – 1) = 0
x (x – 1)2 = 0
either x =1 or x = 0, Hence 2 solutions are possible.

Correct Option: 1 Best Solution (4)