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Question

The complete set of values of a for which the inequality (a1)x2(a+1)x+(a1)0 is true for all x2 is


Your Answer
A
(1,73]
Your Answer
B
(73,)
Your Answer
C
(,73]
Correct Answer
D
[73,)

Solution

The correct option is D [73,)
Since, the given inequality is true for all x2, hence required conditions are f(2)0 and a10
 
f(2)0(a1)4(a+1)2+(a1)0
3a70a[73,)   ...(1)

a10a1   ...(2)

From (1) and (2) 
a[73,)

Alternate Solution:
(a1)x2(a+1)x+(a1)0
ax2+x+1x2x+1
a1+2xx2x+1
a1+2x+1x1
x2
x+1x52
x+1x132
a1+232
a[73,)

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