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Question Number 95634 by i jagooll last updated on 26/May/20

solve ∣x+(1/x)∣ > 2

solve∣x+1x∣>2

Answered by john santu last updated on 26/May/20

solution: this is equivalent to ∣((x^2 +1)/x)∣ > 2 ((x^2 +1)/(∣x∣)) > 2 [ since x^2 +1 >0 ] x^2 +1 > 2∣x∣ ; x^2 −2∣x∣+1 > 0 ∣x∣^2 −2∣x∣+1 > 0 , (∣x∣−1)^2 > 0 ∣x∣ ≠ 1 . answer all x except x =1 and x=−1

solution: thisisequivalentto∣x2+1x∣>2 x2+1∣x∣>2[sincex2+1>0] x2+1>2∣x∣;x2−2∣x∣+1>0 ∣x∣2−2∣x∣+1>0,(∣x∣−1)2>0 ∣x∣≠1.answerallxexceptx=1andx=−1

Commented bypeter frank last updated on 26/May/20

thank you

thankyou

Commented byi jagooll last updated on 26/May/20

thank you

thankyou

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