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If x+y+z=1,xy+yz+zx=-1 & xyz=-1,find the value of x³+y³+z³.?
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If x+y+z=1,xy+yz+zx=-1 & xyz=-1,find the value of x³+y³+z³.?
x^3+y^3+z^3-3xyz= (x + y + z) (x^2 +y^2 + z^2 yz zx xy)
x^3+y^3+z^3=(x +y + z) (x^2+y^2+ z^2yz zx xy) + 3xyz ( Rearranging the terms)
Putting the values,
x^3+y^3+z^3= (1) {(x^2+y^2+ z^2- ( -1)} +3 (-1)
x^3+y^3+z^3= (1) (x^2+y^2+ z^2+1 ) -3 ------------------- Equation1
Now,
x^2+y^2+ z^2
(x+y+z)^2 =x^2+y^2+ z^2+ 2 (xy+yz+zx)
(1)2 =x^2+y^2+ z^2+2(-1)
1 =x^2+y^2+ z^2-2
3=x^2+y^2+ z^2----------------------------- Equation 2
Putting values of 2 on 1, we get
x^3+y^3+z^3= (1) (3+1 ) -3
x^3+y^3+z^3= (1) (4) -3
x^3+y^3+z^3 = 1
This question is part of UPSC exam. View all Class 9 courses
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If x+y+z=1,xy+yz+zx=-1 & xyz=-1,find the value of x³+y³+z³.?
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