|x-1||x+5|=7

解答

∣ x - 1 ∣ ∣ x + 5 ∣ = 7

x = - 6 or x = - 2 - 2 or x = - 2 + 2 or x = 2

十进制

x = - 6, x = - 3.41421 \dots, x = - 0.58578 \dots, x = 2

求解步骤

∣ x - 1 ∣ ∣ x + 5 ∣ = 7

找到正负区间

x < - 5, - 5 \leq x < 1, x \geq 1

对每个区间解不等式

x = - 6 or (x = - 2 - 2 or x = - 2 + 2) or x = 2

x = - 6 or x = - 2 - 2 or x = - 2 + 2 or x = 2

x^{2} + 6 x + 6 = x^{2} + 4 x + 9 + ∣ 2 x - 3 ∣

x^{2} + 3 x + 2 + x + 1 = 0

x^{2} - 4 x + 2 = \frac{( 5 x - 4 )}{3}

∣ x ∣ - 2 ∣ x + 1 ∣ + 3 ∣ x + 2 ∣ = 0

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