fx=8x,fy=18y
gx=y,gy=x
fx=λgx⟹8x=λy
fy=λgy⟹18y=λx
9y4x=xy⟹9y2=4x2
y=±2x/3
then:
2x2/3=6⟹x=±3
solution:
(3,2),(3,−2),(−3,2),(−3,−2)
f(3,2)=f(3,−2)=f(−3,2)=f(−3,−2)=72
f(x,y)=4(6/y)2+9y2
if we take, for example, y =1we get:
f(x,1)=153>72
so,
f(3,2)=f(3,-2)=f(-3,2)=f(-3,-2)=72 are minimums
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