Maximize f=3x + 2y
suject
x^1/2 + y^1/2 = 5

Resp= max = 75

Fait:
L = 3x+2y - h(x^1/2 + y^1/2 -5)
Lx= 3 -h(1/2[1/2x^1/2]) = 0
Ly= 2 - h(1/2[1/2y^1/2]) = 0
x^1/2 + y^1/2 = 5

comme h>0,

y^1/2=x^1/2 -5
3*2x^1/2=2(5-x^1/2)

x^1/2=5/4
y^1/2 = 15/4

J'arrive à 625/16 =\= 75!..
Oú j'ai raté?