The set of values of a for which (a−1)x2−(a+1)x+a−1≥0 is true for all x≥2 is

Given,(a−1)x2−(a+1)x+a−1≥0or ax2−x+1−x2+x+1≥0⇒ a≥x2+x+1x2−x+1=1+2xx2−x+1=1+2x+1x−1                 (1)Let y=x+1/x. Now, y is increasing in [2,∞).  Hence1+2x+1x−1∈1,73For all x≥2 Eq. ( 1) should be true. Hence, a > 7/3 .