Question

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

Answer 1

Answer:

889 6748 7792889 6748 7792889 6748 7792

Step-by-step explanation:

889 6748 7792

Answer 2

$\huge\green{\mathfrak{\underline{\underline{ANSWER}}}}$

${x }^{2} + {y}^{2} + {z}^{2} - xy - yz - zx$

Let us assume that x, y and z have values in -ve.

$= > { - x}^{2} + { - y}^{2} + { - z}^{2} - ( - x)( - y) - ( - y)( - z) - ( - z)( - x) \\ = > {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx$

Now let the values of x, y and z be -4.

${ - 4}^{2} + {( - 4)}^{2} + {( - 4)}^{2} - ( - 4)( - 4) - ( - 4) ( - 4) - ( - 4)( - 4) \\ 16 + 16 + 16 - 16 - 16 - 16 \\ = > 0$

Now let the values of x, y and z be 2,-3, -7 respectively.

${2}^{2} + {( - 3)}^{2} + {( - 7)}^{2} - 2( - 3) - ( - 3)( - 7) - ( - 7)2 \\ = > 4 + 9 + 49 + 6 - 21 + 14 \\ = > 61$

All the about situations proves that:-

${x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx$

is always positive.

HOPE THIS HELPS YOU!!!!!!!!!!

PLEASE MARK IT AS BRAINLIST!!!

#STAY HOME #STAY SAFE