(x^2-5x+6)^2+|3 -|x|| =0 45баллов

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вопрос

To solve this equation, we will first expand the square of the quadratic expression and simplify:

(x^2 - 5x + 6)^2 + |3 - |x|| = 0
(x^4 - 10x^3 + 31x^2 - 30x + 36) + |3 - |x|| = 0

Now we will focus on the absolute value terms.

If x is positive, then |x| = x, and |3 - |x|| = |3 - x|
If x is negative, then |x| = -x, and |3 - |x|| = |3 + x|

So the equation can be split into cases:

If x is positive:
(x^4 - 10x^3 + 31x^2 - 30x + 36) + |3 - x| = 0
(x^4 - 10x^3 + 31x^2 - 30x + 36) + 3 - x = 0
x^4 - 10x^3 + 31x^2 - 31x + 33 = 0

If x is negative:
(x^4 - 10x^3 + 31x^2 - 30x + 36) + |3 + x| = 0
(x^4 - 10x^3 + 31x^2 - 30x + 36) + -(3 + x) = 0
x^4 - 10x^3 + 31x^2 - 27x + 33 = 0

These are the separate equations based on the sign of x. You can solve each equation by factoring, using the quadratic formula, or any other method to find the possible values of x.