Gujarat BoardEnglish MediumSTD 9MathsPolynomials1 Mark
MCQ
If $x + y + z = 0$ then $x^3+y^3+z^3$ is:
✓
$3xyz$
B
$xyz$
C
$2xyz$
D
$0$
✓
Answer
Correct option: A.
$3xyz$
$x^3+y^3+z^3-3 x y z=(x+y+z)\left(x^2+y^2+z^2-x y-y z-z x\right)$
$\Rightarrow x^3+y^3+z^3-3 x y z=(0)\left(x^2+y^2+z^2 x y-y z-z x\right)$
$\Rightarrow x^3+y^3+z^3-3 x y z=0$
$\Rightarrow x^3+y^3+z^3=3 x y z \text { if } x+y+z=0, \text { then } x^3+y^3+z^3 \text { is } 3 x y z$
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