Question

exercițiul 7......... ​

Answer 1

Răspuns:

Explicație pas cu pas:

a) x+y+z=9,  ridicam la patrat aceasta egalitate

(x+y+z)²=9², ⇒x²+y²+z²+2xy+2xz+2yz=81, ⇒x²+y²+z²=81-2·(xy+xz+yz)=81-2·26=81-52=29

b)  Ridicam la patrat egalitatea x-y-z=8, ⇒(x-y-z)²=8², ⇒x²+y²+z²-2xy-2xz+2yz=64, ⇒x²+y²+z²=64+2(xy+xz-yz)=64+2·(-23)=64-46=18

c)  Ridicam la patrat egalitatea x+y+z=25, ⇒(x+y+z)²=25², ⇒x²+y²+z²+2xy+2xz+2yz=625, ⇒2(xy+xz+yz)=625-(x²+y²+z²)=625-327, ⇒

2(xy+xz+yz)=298, ⇒xy+xz+yz=149

d)  Ridicam la patrat egalitatea x+y-z=7, ⇒(x+y-z)²=7², ⇒x²+y²+z²+2xy-2xz-2yz=49, ⇒2(xy-xz-yz)=49-(x²+y²+z²)=49-61, ⇒

2(xy-xz-yz)=-12, ⇒xy-xz-yz=-6