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CBSE Class 10 Answered

If  x+y+z=1.....then 1- 3x² -3y² -3z² + 2x³ +2y³ +2z³ equals to
Asked by shamim.ayanahmad | 26 Dec, 2017, 11:53: AM
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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 | 26 Dec, 2017, 12:23: PM

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