Find all values of a for which the inequality (a - 1)x² - (a + 1)x + a + 1 > O is satisfied for all real x.
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(a−1)x
2
−(a+1)x+a+1>0
For this inequality to hold
(a+1)
2
−4(a+1)(a−1)<0
(a+1)(a+1−4a+4)<0
(a+1)(3a−5)>0⟹a∈(−∞,−1)∪(
3
5
,∞)
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