What is the maximum value of x y + 1 </mrow> </mfrac>

dikcijom2k

dikcijom2k

Answered question

2022-07-08

What is the maximum value of x y + 1 + y x + 1 while 0 x , y 1 ?

Answer & Explanation

Miles Mueller

Miles Mueller

Beginner2022-07-09Added 11 answers

Step 1
When 0 x , y 1 , then
x y + 1 x x + y
y x + 1 y x + y
Adding them we have
x y + 1 + y x + 1 x + y x + y = 1. .
Equality holds when x = 0 and y = 1 or x = 1 and y = 0 and the maximum of 1 is attained.
pouzdrotf

pouzdrotf

Beginner2022-07-10Added 4 answers

Step 1
It is
x y + 1 + y x + 1 1
since
x ( x + 1 ) + y ( y + 1 ) ( x + 1 ) ( y + 1 )
This is equivalent to
0 x ( 1 x ) + ( 1 y ) ( 1 x + y )

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