If x is real, then the expression ` (x^(2) +34x -71)/(x^(2)+2x -7)`

Options

A. `[5, 9]`
B. `(-oo, 5]`
C. `[9, oo)`
D. `R - (5, 9)`

Answer

D

Explanation

Let `y=(x^(2)+34x-71)/(x^(2)+2x-7)`. Then, `x^(2)(y-1) + 2x(y-17)-(7-71)=0`
Since x is real. Therefore, the above equation has real roots.
`therefore" "4(y-17)^(2) + 4(y-1) (7y - 71) ge 0" "["Putting Disc" ge 0]`
`rArr" "y^(2) - 14y + 45 ge 0`
`rArr" "(y-5)(y-9) ge 0 rArr y le 5 or y ge 9 rArr y in R - (5, 9)`