Question

find the maximum value of the expression X by X2 - 5 x + 9 for all real values of x​

Answer 1

Given: The equation x / (x^2 - 5x + 9)

To find: the maximum value of the expression given.

Solution:

• Now we have given the equation as:  x / (x^2 - 5x + 9)

• Let it be y, then:

                y =  x / (x^2 - 5x + 9)

• Cross multiplying it, we get:

                y(x^2 - 5x + 9) = x

• Expanding it, we get:

                x^2 y - 5xy - x + 9y = 0

                yx^2 - (5y+1)x + 9y = 0.

• Now for x to be real, discriminant should be greater than or equal to 0. So:

                b^2 - 4ac ≥ 0

                (5y+1)^2 - 4(y)(9y) ≥ 0

                (5y+1)^2 - 36y^2 ≥ 0

                11y^2 - 10y - 1 ≤ 0

                (11y + 1)(y - 1) ≤ 0

                -1/11 ≤ y ≤ 1

Answer:

           So the maximum value of the expression given 1.