Question

Calulati x^2+y^2+z^2 daca x-y-z=8 si xy+xz-yz=-23

Answer 1

Notam S = x^2 + y^2 + z^2

Din formula trinomului la patrat avem:

(-x+y+z)^2 = x^2 + y^2 + z^2 -2xy -2xz + 2yz) = S - 2(xy+xz-yz) = S - 2*(-23) = S+46 = (-8)^2

S+46 = 64

S = 64-46

S = 18.