1.

for all real valuea of x,the maximum value of the expression x/x2-5x+9 is what?

Answer»

Solution:

Let x/(x2-5x+9) = y
=> yx2 - (5y+1)x + 9y = 0.
For x to be real, discriminant ≥ 0
=> (5y+1)2 - 36y2 ≥ 0
=> 11y2 - 10y - 1 ≤ 0
=> (11y + 1)(y-1) ≤ 0
=> -1/11 ≤ y ≤ 1

Remember: If (x-a)(x-b) ≤ 0, where b>a, then a ≤ x ≤ b.



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