What is the answer to (x^2-5x+6)^2-5|x^2-5x+6|+6=0 ?

The answer to (x^2-5x+6)^2-5|x^2-5x+6|+6=0 is x=(5-sqrt(13))/2 \lor x=1\lor x=4\lor x=(5+sqrt(13))/2

Solve for x: (x^2-5x+6)^2-5|x^2-5x+6|+6=0

The solution is x=(5-sqrt(13))/2 \lor x=1\lor x=4\lor x=(5+sqrt(13))/2

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(x^{2} - 5 x + 6)^{2} - 5 x^{2} - 5 x + 6 + 6 = 0

x = \frac{5 - 13}{2} or x = 1 or x = 4 or x = \frac{5 + 13}{2}

Decimal Notation

x = 0.69722 \dots, x = 1, x = 4, x = 4.30277 \dots

Solution steps

(x^{2} - 5 x + 6)^{2} - 5 x^{2} - 5 x + 6 + 6 = 0

Find positive and negative intervals

x \leq 2, 2 < x < 3, x \geq 3

Solve the inequality for each interval

(x = \frac{5 - 13}{2} or x = 1) or No Solution or (x = 4 or x = \frac{5 + 13}{2})

x = \frac{5 - 13}{2} or x = 1 or x = 4 or x = \frac{5 + 13}{2}

∣ 2 x - 3 ∣ + ∣ 4 - x ∣ = ∣ x + 1 ∣

∣ x - 2 ∣ + ∣ x + 6 ∣ = 8

x^{2} + 1 = x^{2} - 3 x

∣ x - 3 ∣ = 4 - x

(3 x - 2) 2 - 5 ∣ 3 x - 2 ∣ - 6 = 0

What is the answer to (x^2-5x+6)^2-5|x^2-5x+6|+6=0 ?
The answer to (x^2-5x+6)^2-5|x^2-5x+6|+6=0 is x=(5-sqrt(13))/2 \lor x=1\lor x=4\lor x=(5+sqrt(13))/2
Solve for x: (x^2-5x+6)^2-5|x^2-5x+6|+6=0
The solution is x=(5-sqrt(13))/2 \lor x=1\lor x=4\lor x=(5+sqrt(13))/2