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The-value-of-x-satisfying-the-inequalities-2x-1-x-1-4-x-2-4-x-2-x-4-4-0-

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Question Number 72830 by Tip Top last updated on 03/Nov/19
The value of x satisfying the inequalities (((2x−1)(x−1)^4 (x−2)^4 )/((x−2)(x−4)^4 ))≤ 0
Thevalueofxsatisfyingtheinequalities(2x−1)(x−1)4(x−2)4(x−2)(x−4)4⩽0
Answered by MJS last updated on 03/Nov/19
defined for R\{2, 4} (((x−1)^4 (x−2)^4 )/((x−4)^4 ))≥0 ∀ x∈R\{4} ((2x−1)/(x−2))≤0 2x−1≥0∧x−2<0 ∨ 2x−1≤0∧x−2>0 ⇒ (1/2)≤x<2
definedforR∖{2,4}(x−1)4(x−2)4(x−4)4⩾0∀x∈R∖{4}2x−1x−2⩽02x−1⩾0∧x−2<0∨2x−1⩽0∧x−2>0⇒12⩽x<2
Answered by Tanmay chaudhury last updated on 03/Nov/19
(x−1)^4 ,(x−2)^4 and (x−4)^4 even power so they are always +ve . x≠2 x≠ 4 critical value of x=(1/2)=0.5 and 2 f(x)=((2x−1)/((x−2)))×[(((x−1)(x−2))/((x−4)))]^4 when x>2 f(x)>0 when x<0.5 f(x)>0 when 2>x>0.5 f(x)<0 solution x∈ [0.5, 2) pls check
(x−1)4,(x−2)4and(x−4)4evenpowersotheyarealways+ve.x≠2x≠4criticalvalueofx=12=0.5and2f(x)=2x−1(x−2)×[(x−1)(x−2)(x−4)]4whenx>2f(x)>0whenx<0.5f(x)>0when2>x>0.5f(x)<0solutionx∈[0.5,2)plscheck

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