Question

If x+y+z=0,xsquare+ysquare+zsquare=12find xy+yz+zx

Answer 1

Step-by-step explanation:

(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx

0=12+2(xy+yz+zx)

xy+yz+zx=-12/2=-6

Answer 2

The value of xy + yz + zx is -6.

Step-by-step explanation:

Given:

• x + y + z = 0
• x² + y² + z² = 12

To find:

• xy + yz + zx

Solution:

In this problem, an important algebraic identity is used.

☯ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

Let's solve the problem!

→ x + y + z = 0 [Given]

→ (x + y + z)² = 0 [Squaring the equation]

→ x² + y² + z² + 2xy + 2yz + 2zx = 0 [Using Identity]

→ 12 + 2xy + 2yz + 2zx = 0

→ 2xy + 2yz + 2zx = -12

→ 2(xy + yz + zx) = -12 [Taking 2 as common]

→ xy + yz + zx = -6

Hence, the value of xy + yz + zx is -6.