Question

Prove that x² + y² + z² - xy - yz - zx is always positive.​

Answer 1

Prove that : x2+ y2 + z2 - xy - yz - zx is always positive.

SOLUTION

x2 + y2 + z2 - xy - yz - zx

= 2(x2 + y2 + z2 - xy - yz - zx)

= 2x2 + 2y2 + 2z2 - 2xy - 2yz - 2zx

= x2 + x2 + y2 + y2 + z2 + z2 - 2xy - 2yz - 2zx

= (x2 + y2 - 2xy) + (z2 + x2 - 2zx) + (y2 + z2 - 2yz)

= (x - y)2 + (z - x)2 + (y - z)2

Since square of any number is positive, the given equation is always positive

Step-by-step explanation:

I HOPE IT CAN HELP YOU ❤️

PLS MAKE ME BRAINLIST

Answer 2

Answer:

See the picture.

Step-by-step explanation:

Hope this helps.