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Question Number 62676 by bshahid010@gmail.com last updated on 24/Jun/19

Commented by kaivan.ahmadi last updated on 24/Jun/19

if tanx=n>0⇒ n^2 +an+n+a−3<0⇒a(n+1)<3−n^2 −n⇒ a<((3−n−n^2 )/(n+1))

iftanx=n>0⇒n2+an+n+a−3<0⇒a(n+1)<3−n2−n⇒a<3−n−n2n+1

Answered by ajfour last updated on 24/Jun/19

If t^2 +(a+1)t+(a−3)<0 for every t∈(0,∞) ⇒ a∈{ }.

Ift2+(a+1)t+(a−3)<0foreveryt∈(0,∞)⇒a∈{}.

Commented by kaivan.ahmadi last updated on 24/Jun/19

if t=1⇒ 1+a+1+a−3<0⇒2a<1⇒a<(1/2)

ift=1⇒1+a+1+a−3<0⇒2a<1⇒a<12

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