Let the sum of the maximum and the minimum values of the function f ( x ) = 2 x 2 + 3 x + 8 2 x 2 − 3 x + 8 be n m , where gcd ( m , n ) = 1 . Then m + n is equal to :

Question

Let the sum of the maximum and the minimum values of the function f ( x ) = 2 x 2 + 3 x + 8 2 x 2 − 3 x + 8 ​ be n m ​ , where gcd ( m , n ) = 1 . Then m + n is equal to :

TestHub · Accepted Answer

​ y = 2 x 2 + 3 x + 8 2 x 2 − 3 x + 8 ​ x 2 ( 2 y − 2 ) + x ( 3 y + 3 ) + 8 y − 8 = 0 use D ≥ 0 ( 3 y + 3 ) 2 − 4 ( 2 y − 2 ) ( 8 y − 8 ) ≥ 0 ( 11 y − 5 ) ( 5 y − 11 ) ≤ 0 ⇒ y ∈ [ 11 5 ​ , 5 11 ​ ] y = 1 is also included ​

Mathematics - Functions Question with Solution | TestHub

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