Log in to add a comment

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

X² + y² + z² -xy - xz - yz = 0

multiplying 2 on both sides

2x² + 2y² + 2z² - 2xy - 2xz - 2yz = 0

x² + y² - 2xy+ x² + z² - 2xz + z² + y² - 2yz = 0

(x - y)² + (x - z)² + (y - z)² = 0

so the value are in square so they can't be negative so they must be indivudually zero to satisfy the equation

so x - y = 0 ⇒ x = y

x - z = 0 ⇒ x = z

y - z = 0 ⇒ y = z

so hence x = y = z__proved__

multiplying 2 on both sides

2x² + 2y² + 2z² - 2xy - 2xz - 2yz = 0

x² + y² - 2xy+ x² + z² - 2xz + z² + y² - 2yz = 0

(x - y)² + (x - z)² + (y - z)² = 0

so the value are in square so they can't be negative so they must be indivudually zero to satisfy the equation

so x - y = 0 ⇒ x = y

x - z = 0 ⇒ x = z

y - z = 0 ⇒ y = z

so hence x = y = z