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If x is real, and k=(x^2)-x+1/(x^2)+x+1, then : (a) 1/3 =5 (c) k

If x is real, and k=(x^2)-x+1/(x^2)+x+1, then : (a) 1/3<=k=<3 (b) k>=5 (c) k<=0 (d) none of these

Grade:12th pass

1 Answers

Abhishek Doyal
askIITians Faculty 25 Points
10 years ago
k=x^2-x+1/x^2+x+1 eq 1
cross muitiply then arrange the eq 1
(k-1)x^2+(k+1)x+k-1=0 so x is real then D>=0
D=(k+1)^2-4(k-1)^2>=0
k^2+2k+1-4k^2+8k-4>=0
-3k^2+10k-3>=0
muiltiply by -1
3k^2-10k+3<=0
solve the inequality 1/3<=k<=3


Abhishek doyal
IIT Bombay
Askiitian tutor

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