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Question

Find all values of a for which the inequality (a1)x2(a+1)x+a+1>0 is satisfied for all real x.

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Solution

(a1)x2(a+1)x+a+1>0

For this inequality to hold

(a+1)24(a+1)(a1)<0

(a+1)(a+14a+4)<0

(a+1)(3a5)>0a(,1)(53,)

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