Question

Calculați x+y+z,stiind ca x,y,z € R si x la a doua+y la a doua+z la a doua=216 si xy+yz+zx=230

Answer 1

Folosim relatia (x+y+z)²= x² + y² + z² +2xy +2yz+2xz

(x+y+z)²= x² + y² + z² +2(xy +yz+xz)

Inlocuim valorile in relatie:

(x+y+z)²=216 + 2*230=216+460 ⇒ (x+y+z)²=676=26² ⇒ x+y+z=26