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Lagrange multiplier

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f(x,y,z)=x^2+y^2+z^2, x-y=1, y^2-z^2=1
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This solution helps with a Lagrange multiplier.

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f(x,y,z) = x^2 + y^2 + z^2
x - y = 1
y^2 - z^2 = 1

Since there are two constraints, we need to solve:
?f=??g+ ??h
g(x,y,z) = x - y, h(x,y,z) = y^2 - z^2

?f= <f_x,f_y,f_z> = <2x, 2y, 2z>
?g= <g_x,g_y,g_z> = <1, -1, 0>
?h= <h_x,h_y,h_z> = <0, 2y, -2z>

So, we need to solve the system of equations:
f_x= ?g_x+ ?h_x: 2x= ? (1)
f_y= ?g_y+ ?h_y: 2y= -?+2y? (2)
f_z= ?g_z+ ?h_z: ...

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