Question

Find the maximum value of the expression 1/(x^2+5x+10)

Answer 1

maximum value of 1/(x² + 5x + 10) is 4/15

we have to find maximum value of 1/(x² + 5x + 10)

if we get minimum value of (x² + 5x + 10) then obviously maximum value of given expression can be found.

let y = x² + 5x + 10

x² + 5x + 10 - y = 0

discrimination, D = (5)² - 4(10 - y) ≥ 0 for all real value of x.

⇒25 - 40 + 4y ≥ 0

⇒-15 + 4y ≥ 0

⇒ y ≥ 15/4

hence, minimum value of y = 15/4

then, maximum value of 1/y or 1/(x² + 5x + 10) = 1/(15/4) = 4/15

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Answer 2

Answer:

the value of the explanation 10 5