Question

if x+y+z=10 and x^2+y^2+z^2=40,then xy +yz+zx is equal to:
(a)60
(b)30
(c)40
(d)20

Answer 1

There is an identity where (x+y+z)=x^2+y^2+z^2 +2xy+2yz+2zy
substituting the values
(10)^2=40+2(x^2+y^2+z^2 +2xy+2yz+2zy)
60=2(x^2+y^2+z^2 +2xy+2yz+2zy)
(x^2+y^2+z^2 +2xy+2yz+2zy)=30
option B is correct