(x-y)² + (χ-z)² + (y-z)² = 2 (χ² + y² + z² - χz -χy -zy)?
How: (x-z)² + (χ-z)² + (χ-z)² = 2 (χ² + y² + z² - χz -χy -zy)
math
Still have questions? Get your answers by asking now.
How: (x-z)² + (χ-z)² + (χ-z)² = 2 (χ² + y² + z² - χz -χy -zy)
math
Copyright © 2024 1QUIZZ.COM - All rights reserved.
Answers & Comments
Verified answer
(x-y)² + (x-z)² + (y-z)² = 2 (x² + y² + z² - xz -xy -zy)
(x-y)² + (x-z)² + (y-z)²
= x² - 2xy + y² + x² - 2xz + z² + y² - 2yz +z²
= 2x² + 2y² + 2z² - 2xy -2xz - 2yz
= 2 (x² + y² + z² - xz -xy -zy) = RHS
LS =(x-y)² + (χ-z)² + (y-z)²
= {x^2 -2xy +y^2} +{x^2 -2xz +z^2} + {y^2 -2yz +z^2}
= 2(x^2+y^2+z^2) -2(xy+yz+zx)
= 2{x^2+y^2+z^2 -xz -xy -zy) = RS
(χ-y)² + (χ-z)² + (y-z)² = (χ-y)(χ-y) + (χ-z)(χ-z) + (y-z)(y-z)
= χ² - 2χy + y² + χ² - 2χz + z² + y² - 2yz + z²
= χ² + χ² + y² + y² + z² + z² - 2χy - 2χz - 2yz
= 2χ² + 2y² + 2z² - 2χy - 2χz - 2yz = 2*( χ² + y² + z² - χy -χz - yz )
= 2*( χ² + y² + z² -χz - χy - zy )
(x-y)² + (χ-z)² + (y-z)²
x² -2xy + y² + x² -2xz + z² + y² -2yz + z²
2x²-2xy + 2y² -2xz +2z² -2yz
=2 (χ² + y² + z² - χz -χy -zy)