Question

if x+y+z=0,x square + y square +z square=12, then the value of xy+yz+zx

Answer 1

x square + y square + z square =12
x square = y square = z square = 2square
xy+yz+zx=48

Answer 2

x+y+z=0

x²+y²+z²=12

we know that ,

(x+y+z)²= x²+y²+z²+2(xy+yz+zx)

0²=12+2(xy+yz+zx)

-12= 2(xy+yz+zx)

-6= (xy+yz+zx)

Hence value of xy+yz+zx is -6