Does |x^2-3x+3|=3 have a solution?

Answer 1

1. Eliminate the absoulute value :

x ^ 2 - 3 x + 3 = 3

x ^ 2 - 3 x + 3 = - 3

______________________

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.

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x ^ 2 - 3 x = 0

and equation

x ^ 2 - 3 x + 6 = 0

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quadratic equation online

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