Menu Close

For-all-real-values-of-x-solve-the-inequality-1-x-3-x-6-2x-3-5-1-4-




Question Number 41095 by Necxx last updated on 02/Aug/18
For all real values of x solve the  inequality   ∣((1−x^3 )/(x^6 −2x^3 +5))∣≤(1/4)
Forallrealvaluesofxsolvetheinequality1x3x62x3+5∣⩽14
Answered by ajfour last updated on 02/Aug/18
let x^3 −1=t  ⇒  ∣(t/(t^2 +4))∣≤(1/4)  or       −(1/4)≤ (t/(t^2 +4)) ≤(1/4)  or    t^2 +4t+4 ≥ 0     and          t^2 −4t+4 ≥ 0  ⇒  t∈(−∞,∞)    the same for x.
letx31=ttt2+4∣⩽14or14tt2+414ort2+4t+40andt24t+40t(,)thesameforx.

Leave a Reply

Your email address will not be published. Required fields are marked *