Find the conditional extremum of function z = XY under given condition x + y = 2

Max 1 min - 1
Mean form
u=x+y-2
z(x,y,t)=xy+t(x+y-2)
z'(x,y,t)x=y+t=0
z'(x,y,t)y=x+t=0
z'(x,y,t)t=x+y-2=0
We get x = y = 1
Z''X=0
Z''Y=0
Z''T=0
The maximum value is obtained in (1,1)
one

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