If x=y=z and ∣∣×21+x3yy21+y3zz21+z3∣∣=0 , then prove that xyz=−1 .

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If {x}{y}{z} and {|^{{2}}{1}+{x}^{{3}}{y}{y}^{{2}}{1}+{y}^{{3}

Question

If $x \neq = y \neq = z$ and $∣ ∣ \times^{2} 1 + x^{3} y y^{2} 1 + y^{3} z z^{2} 1 + z^{3} ∣ ∣ = 0$ , then prove that $x y z = - 1$ .

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Asher Discussed

x \neq = y \neq = z

and

∣ ∣ \times^{2} 1 + x^{3} y y^{2} 1 + y^{3} z z^{2} 1 + z^{3} ∣ ∣ = 0

, then prove that

x y z = - 1

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Question Text

x \neq = y \neq = z

and

∣ ∣ \times^{2} 1 + x^{3} y y^{2} 1 + y^{3} z z^{2} 1 + z^{3} ∣ ∣ = 0

, then prove that

x y z = - 1