1.

The set of values of a for which ` (a - 1) x^(2) - (a + 1) x + a - 1` `ge 0 ` ture for all ` x ge 2` isA. `(-infty, 1)`B. `(1, (7)/(3))`C. `((7)/(3), infty)`D. none of these

Answer» Correct Answer - 3
Given,
`(a - 1) x^(2) - (a + 1) x + a - 1 ge 0 `
or ` a(x^(2) - x + 1) - (x^(2) + x + 1) ge 0 `
` rArr ge (x^(2) + x + 1)/(x^(2) - x + 1) = (2x)/(x^(2) - x + 1)`
` = 1 + (2)/(x + (1)/(x) - 1)`
Let y = x + 1/x , Now , y is increasing in ` [ 2, infty)` . Hence,
` = 1 + (2)/(x + (1)/(x) - 1)in (1 , (7)/(3))`
For all ` x ge 2,` Eq (1). should be true . Hence , ` a ge 7//3)`


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