If x + y = a , then the maximum value of x &#x2217;<!-- ∗ --> y is when

Ellie Benjamin 2022-06-30 Answered
If x + y = a, then the maximum value of x y is when x = y = a / 2. ( x , y are positive numbers)
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Answers (2)

persstemc1
Answered 2022-07-01 Author has 18 answers
x y = ( x + y ) 2 ( x y ) 2 4 = a 2 ( x y ) 2 4 a 2 4
with equaloity iff x y = 0

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Sylvia Byrd
Answered 2022-07-02 Author has 6 answers
With
y = a x
we get
x ( a x ) = a x x 2 = ( x 2 a x + a 2 4 a 2 4 ) = ( x a 2 ) 2 + a 2 4 a 2 4

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