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Question Number 78335 by john santu last updated on 16/Jan/20
find the solution of (x/((x−2)^3 +(x−3)^3 −1)) ≥ 0
findthesolutionofx(x−2)3+(x−3)3−1⩾0
Answered by MJS last updated on 16/Jan/20
⇒ x>0∧((x−2)^3 +(x−3)^3 −1)>0 ∨ x=0∧((x−2)^3 +(x−3)^3 −1)≠0 ∨ x<0∧((x−2)^3 +(x−3)^3 −1)<0 (x−2)^3 +(x−3)^3 −1=(x−3)(2x^2 −9x+12) ⇒ { ((((x−2)^3 +(x−3)^3 −1)<0; x<3)),((((x−2)^3 +(x−3)^3 −1)>0; x>3)) :} ⇒ x≤0∨x>3
⇒x>0∧((x−2)3+(x−3)3−1)>0∨x=0∧((x−2)3+(x−3)3−1)≠0∨x<0∧((x−2)3+(x−3)3−1)<0(x−2)3+(x−3)3−1=(x−3)(2x2−9x+12)⇒{((x−2)3+(x−3)3−1)<0;x<3((x−2)3+(x−3)3−1)>0;x>3⇒x⩽0∨x>3
Commented by john santu last updated on 16/Jan/20
thanks sir
thankssir

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