Question

Fie x,y,z apartin lui R astfel incat x+y+z=1 Si (x+y)(y+z)(z+x)=14. Calculați xy+yz+zx-xyz.
Va rog frumos sa ma ajutati.

Answer 1

x+y+z=1=> x+y=1-z
x+z=1-y
y+z=1-x
(x+y)(x+z)(z+y)=14
(1-z)(1-y)(1-x)=(1-y-z+zy)(1-x)= 1-x-y+xy-z+zx+zy-xyz=1-(x+y+z)+xy+zx+zy-xyz=1-1+xy+zx+zy-xyz=>
xy+yz+xz-xyz=14