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Question Number 111623 by weltr last updated on 04/Sep/20

(x−2)(x+3)(x−1)^2 ≥ 0

(x−2)(x+3)(x−1)2⩾0

Commented by ZiYangLee last updated on 04/Sep/20

x≤−3 ∪ x≥2?

x⩽−3∪x⩾2?

Commented by weltr last updated on 04/Sep/20

the answer must be (−∞, −3] ∪ {1} ∪ [2, +∞)

theanswermustbe(−∞,−3]∪{1}∪[2,+∞)

Answered by Her_Majesty last updated on 04/Sep/20

(x−1)^2 ≥0∀x∈R but (x−1)^2 =0; x=1 (x−2)(x+3)≥0 ⇒ x≤−3 ∨ x≥2 ∨x=1

(x−1)2⩾0∀x∈Rbut(x−1)2=0;x=1(x−2)(x+3)⩾0⇒x⩽−3∨x⩾2∨x=1

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