Question

if x+y+z=4 and x^2+y^2+z^2=10,find the value of xy+yz+zx.​

Answer 1

Answer :-

_____________________

Given , x + y + z = 4

and , x² + y² + z² = 10

To find , xy + yz + zx

Salutation ,

x² + y² + z² = 10

( x + y + z )² - 2 ( xy + yz + zx ) = 10

4² - 2 ( xy + yz + zx ) = 10

16 - 2 ( xy + yz + zx ) = 10

- 2 ( xy + yz + zx ) = 10 - 16

- 2 ( xy + yz + zx ) = - 6

2 ( xy + yz + zx ) = 6

( xy + yz + zx ) = 6 / 2

( xy + yz + zx ) = 3

•°• The value of 2 ( xy + yz + zx ) is 3.