Mathematics
dee3
2

If x^5y^4z^2 <0 , which of the following must be true? I xy <0 II yz <0 III xz <0

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lyssie11234

[latex]x^5y^4z^2 < 0\\\\y^4\geq0\ for\ y\in\mathbb{R}\\\\z^2\geq0\ for\ y\in\mathbb{R}\\\\x^5 > 0\ for\ y\in\mathbb{R^+}\ and\ x^5 < 0\ for\ x\in\mathbb{R^-}\\\\------------------------------\\\\x^5\underbrace{y^4z^2}_{> 0} < 0\iff x^5 < 0\Rightarrow xy < 0\ \wedge\ xz < 0\\\\------------------------------\\\\Answer:I\ xy < 0\ and\ III\ xz < 0.[/latex]

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