Not sure what I'm doing wrong here.....when I put into wolfram, it said the answer was (1,1,sqrt(2))

Find the extreme values of

f(x,y,z)=xyz

x^2+y^2+z^2=4

g1=x^2+y^2+z^2-4

x+y=2

g2=x+y-2

so I took the gradient of the function to get:

grad f=(yz)i+(xz)j+(xy)k

grad g1=(2x)i+(2y)j+(2z)k

grad g2=i+j

gradf=λgrad g1+μgrad g2

(yz)i+(xz)j+(xy)k=(2xλ+μ)i+(2xλ+μ)j+(2zλ)k