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Grade 9Magical Mathematics[Interesting Approach]

If x+y+z=1 Then (1-3x^2-3y^2-3z^2+2x^3+2y^3+2z^3)=?

Leo Pixie

12 Years agoGrade 9

1 Answer

Arun Kumar

12 Years ago

Hello Student,

$\\(1-3x^2-3y^2-3z^2+2x^3+2y^3+2z^3) \\=>1-3(\sum x^2)+2(\sum x^3) \\(\sum x)^3=(\sum x^3)+3(\sum xy)-3xyz=1 \\(\sum x)^2=(\sum x^2)+2(\sum xy)=1 \\=>(1-3x^2-3y^2-3z^2+2x^3+2y^3+2z^3)=2*3xyz$

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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