The teacher will be very surprised to see your correct solution 😉
/1 2*y\ / z2 4*y2 y*z\ |-- - ---|*|--- + ---- + ---| = 0 \10 5 / \100 25 25/
(1/10 - 2*y/5)*(y*z/25 + 4*y2/25 + z2/100) = 0