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

解答

(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}

十进制

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

求解步骤

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

找到正负区间

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

对每个区间解不等式

(x = \frac{5 - 13}{2} or x = 1) or 无解 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