Question

find the value of x cube + y cube + Z cube minus 3 x y z if X + Y + Z is equal to 12 and X square + Y square + Z square is equal to 70​

Answer 1

To find :

x3 + y3 + z3 - 3xyz

Given:

x + y + z = 12 ------ (i)

x2 + y2 + z2 = 70 -------(ii)

Identities used :

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

x3+y3+z3 -3xyz = (x+y+z) (x2+y2+z2-xy-yz-xz)

Solution :

x + y + z = 12

squaring both sides

[ Here the identity is also used ]

x2 + y2 + z2 +2( xy + yz + xz ) = 144

70 +2( xy + yz + xz ) = 144. ( by ii )

2 ( xy + yz + xz ) = 74

xy + yz + xz. = 37

-----(iii)

by applying identity

x3 + y3 + z3 -3xyz

= (x+y+z) (x2 +y2 +z2 - xy -yz - xz )

= ( 12 ) ( 70 - ( xy + yz + xz ) [ by i n ii ]

= ( 12 ) ( 70 - 37 ) [ by iii ]

= ( 12 ) ( 33 )

= 396

Hope this ans would help you

Thank u ☺️☺️

Answer 2

Answer:

hope this answer helps you