Does |x^2-3x+3|=3 have a solution?
1. Eliminate the absoulute value :
x ^ 2 - 3 x + 3 = 3
x ^ 2 - 3 x + 3 = - 3
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x ^ 2 - 3 x + 3 = 3 Subtract 3 to both sides
x ^ 2 - 3 x + 3 - 3 = 3 - 3
x ^ 2 - 3 x = 0
x ( x - 3 ) = 0
Solutions :
x = 0 and x = 3
x ^ 2 - 3 x + 3 = - 3 Add 3 to both sides
x ^ 2 - 3 x + 3 + 3 = - 3 + 3
x ^ 2 - 3 x + 6 = 0
Solutions :
3 / 2 + i * sqrt ( 15 ) / 2
and
3 / 2 - i * sqrt ( 15 ) / 2
So real solutions are :
x = 0 and x = 3
P.S.
If you don't know how to solve equation
x ^ 2 - 3 x = 0
and equation
x ^ 2 - 3 x + 6 = 0
in google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratioc Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type your equation
and click option: solve it
You will see solution step by step.