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Column I contain rational algebraic expr...

Column I contain rational algebraic expressions and ColumnII contains possible integers which lie in their range. Match the entries of Column I with one or more entries of the elements of Column II.

Text Solution

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`(A)to(p),(B)to(p,q,r,s),(C)t(p,q,s)`
(A)`y=(x^(2)-2x+9)/(x^(2)+2x+9)impliesx^(2)y+2xy+9y=x^(2)-2x+9`
`implies(y-1)x^(2)+2x(y+1)+9(y-1)=0`
`:' x epsilonR`
`:.4(y+1)^(2)-4.9.(y-1)^(2)ge0`
`=(y+1)^(2)-(3y-3)^(2)ge0`
`implies(4y-2)(-2y+4)ge0`
`implies(2y-1)(y-2)le0`
`:.1/2leyle2impliesy=1,2(p)`
(B)`:'y=(x^(2)-3x-2)/(2x-3)implies2xy-3y=x^(2)-3x-2`
`impliesx^(2)-x(3+2y)+3y-2=0 :'x epsioonR`
`:.(3+2y)^(2)-4.1.(3y-2)ge0`
`implies4y^(2)+17ge0`
`:.y epsilon R(p,q,r,s)`
(C)`:' y=(2x^(2)-2x+4)/(x^(2)-4x+3)`
`impliesx^(2)y-4xy+3y=2x^(2)-2x+4`
`impliesx^(2)(y-2)+2x(1-2y)+3y-4=0`
`:'x epsionR`
`:.4(1-2y)^(2)-4(y-2)(3y-4)ge0`
`implies(4y^(2)-4y+1)-(3y^(2)-10y+8)ge0`
`impliesy^(2)+6y-7ge0`
`implies(y+7)(y-1)ge0`
`:.yle-7` or `yge1(p,q,s)`
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