If  x+y+z=1.....then 1- 3x² -3y² -3z² + 2x³ +2y³ +2z³ equals to

Asked by shamim.ayanahmad | 26th Dec, 2017, 11:53: AM

Expert Answer:

begin mathsize 16px style Given space that
straight x plus straight y plus straight z equals 1
squaring space on space both space sides comma
open parentheses straight x plus straight y plus straight z close parentheses squared equals 1
straight x squared plus straight y squared plus straight z squared plus 2 xy plus 2 yz plus 2 xz equals 1
straight x squared plus straight y squared plus straight z squared equals 1 minus 2 xy minus 2 yz minus 2 xz........... left parenthesis 1 right parenthesis
straight x plus straight y plus straight z equals 1
Taking space cubes space on space both space sides comma
open parentheses straight x plus straight y plus straight z close parentheses cubed equals 1
straight x cubed plus straight y cubed plus straight z cubed plus left parenthesis straight x plus straight y plus straight z right parenthesis left parenthesis xy plus yz plus zx right parenthesis equals 1
straight x cubed plus straight y cubed plus straight z cubed plus 1 cross times left parenthesis xy plus yz plus zx right parenthesis equals 1
straight x cubed plus straight y cubed plus straight z cubed equals 1 minus open parentheses xy plus yz plus zx close parentheses................ left parenthesis 2 right parenthesis
Consider comma
1 minus 3 straight x squared minus 3 straight y squared minus 3 straight z squared plus 2 straight x cubed plus 2 straight y cubed plus 2 straight z cubed
equals 1 minus 3 open parentheses straight x squared plus straight y squared plus straight z squared close parentheses plus 2 open parentheses straight x cubed plus straight y cubed plus straight z cubed close parentheses
equals 1 minus 3 open parentheses 1 minus 2 xy minus 2 yz minus 2 xz close parentheses plus 2 open square brackets 1 minus open parentheses xy plus yz plus zx close parentheses close square brackets space space space space space from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis
equals 1 minus 3 plus 6 xy plus 6 yz plus 6 zx plus 2 minus 2 xy minus 2 yz minus 2 zx
equals 2 xy plus 2 yz plus 2 zx
end style

Answered by Sneha shidid | 26th Dec, 2017, 12:23: PM