Finding maxima of $x^2+y^2+z^2$ subject to conditions $\frac{x^2}{4}+\frac{y^2}{5}+\frac{z^2}{25} = 1 $ and $z=x+y$
Now I form $F(x,y,z, \lambda_1 , \lambda_2 )= x^2+y^2+z^2 + \lambda_1(\frac{x^2}{4}+\frac{y^2}{5}+\frac{z^2}{25} - 1 ) + \lambda_2(z-(x+y)) = 0 $
Partially differentiating w.r.t x,y,z we get
$f_x = 2x + \lambda_1\frac{x}{2} + \lambda_2 = 0$
$f_y = 2y + \lambda_1\frac{2y}{5} + \lambda_2 = 0$
$f_z = 2z + \lambda_1\frac{2z}{25} - \lambda_2 = 0$
how do I solve ?