find value of x + Y + Z if X square + Y square + Z square equal to 18

1.	find value of x + Y + Z if X square + Y square + Z square equal to 18 and xy + Y Z plus ZX is equals to 9
Answer» ANSWER: $\green{x+y+z=6}$ Step-by-step explanation: $\boxed{<klux>GIVEN</klux>}$ $x {}^{2} + y {}^{2} + z {}^{2} = 18$ $xy + yz + zx = 9$ $\boxed{Tofind}$ value of $x + y + z$ $\boxed{Answer}$ using identity $(x + y + z) {}^{2} = x {}^{2} + y {}^{2} + z {}^{2} + 2xy + 2yz + 2zx$ $(x + y + z \: ) = x {}^{2} + y {}^{2} + z {}^{2} + 2(xy + yz + zx)$ now PUTTING the given values, we GET $(x + y + z) {}^{2} = 18 + 2(9)$ $(x + y + z) {}^{2} = 18 + 18$ $(x + y + z) {}^{2} = 36$ $x + y + z = \sqrt{36}$ $x + y + z = 6$