AkankshaGMAT1989
Hi
Bunuel and
bb sir,
I need your help to solve the following equation. It is part of a larger DS question.
|X| + X^2 = 2X
My solution is:
If assume cases here:
1. |X| = X
then the equation becomes >>> X+X^2 =2X
=X^2 -X = 0
= X(X-1) = 0
2 possible values of X that are X=0 or X =1
Case 2: |X| = - X
now, LHS is -X + X^2
Should RHS also be -2X or it should remain +2X because the answer changes with this consideration.
Thanks in advance.
You are replacing |x| with -x, when x < 0, but why should you replace x with -x? So, the answer to your question is NO.
|x| + x^2 = 2x
When x < 0, then |x| = -x, and in this case we'd get -x + x^2 = 2x, which gives x = 0 or x = 3. Discard both solutions because neither 0 nor 3 is in the range we consider (x < 0).
When x >= 0, then |x| = x, and in this case we'd get x + x^2 = 2x, which gives x = 0 or x = 1. Both solutions are valid because both 0 and 1 are in the range we consider (x >= 0).
So, |x| + x^2 = 2x has two solutions only x = 0 or x = 1.