InterviewSolution
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InterviewSolution
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If G and L are the greatest and least values of the expression`(2x^(2)-3x+2)/(2x^(2)+3x+2), x epsilonR` respectively. If `L^(2)ltlamdaltG^(2), lamda epsilon N` the sum of all values of `lamda` isA. 1035B. 1081C. 1225D. 1176 |
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Answer» Correct Answer - D Let `y=(2x^(2)-3x+2)/(2x^(2)+3x+2)` `implies2x^(2)y+3xy+2y=2x^(2)-3x+2` `implies2(y-1)x^(2)+3(y+1)x+2(y-1)=0` As `x epsilonR` `:.Dge0` `=9(y+1)^(2)-4.2(y-1).2(y-1)ge0` `implies9(y+1)^(2)-16(y-1)^(2)ge0` `implies(3y+3)^(2)-(4y-4)^(2)ge0` `implies(7y-1)(7-y)ge0` `implies(7y-1)(y-7)le0` `:.1/7leyle7` `:.G=7` and `L=1/7` `:.GL=1` NOw `(G^(100)+L^(100))/2ge(GL)^(100)implies(G^(100)+L^(100))/2ge1` `impliesG^(100)+L^(100)ge2` We have `L^(2)lt lamdalt G^(2)` `(1/7)^(2)ltlamdalt 7^(2)` `implies1/49lt lamdalt 49` `implies lamda=1,2,3,..48` as `lamda epsilon N` `:.` Sum of all values of `lamda=1+2+3+.............+48=(48xx49)/2=1176` |
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