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Question Number 161242 by HongKing last updated on 14/Dec/21

x ; y ; z < 0  (x^3 /( (√(yz)))) = -3  ;  (y^3 /( (√(xz)))) = -6  ;  (z^3 /( (√(xy)))) = -8  find  x∙y∙z = ?

$$\mathrm{x}\:;\:\mathrm{y}\:;\:\mathrm{z}\:<\:\mathrm{0} \\ $$$$\frac{\mathrm{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{yz}}}\:=\:-\mathrm{3}\:\:;\:\:\frac{\mathrm{y}^{\mathrm{3}} }{\:\sqrt{\mathrm{xz}}}\:=\:-\mathrm{6}\:\:;\:\:\frac{\mathrm{z}^{\mathrm{3}} }{\:\sqrt{\mathrm{xy}}}\:=\:-\mathrm{8} \\ $$$$\mathrm{find}\:\:\mathrm{x}\centerdot\mathrm{y}\centerdot\mathrm{z}\:=\:? \\ $$

Answered by mr W last updated on 15/Dec/21

((x^3 y^3 z^3 )/( (√(x^2 y^2 z^2 ))))=−3×6×8  ((x^3 y^3 z^3 )/( −xyz))=−3×6×8  (xyz)^2 =3×6×8=12^2   ⇒xyz=−12

$$\frac{{x}^{\mathrm{3}} {y}^{\mathrm{3}} {z}^{\mathrm{3}} }{\:\sqrt{{x}^{\mathrm{2}} {y}^{\mathrm{2}} {z}^{\mathrm{2}} }}=−\mathrm{3}×\mathrm{6}×\mathrm{8} \\ $$$$\frac{{x}^{\mathrm{3}} {y}^{\mathrm{3}} {z}^{\mathrm{3}} }{\:−{xyz}}=−\mathrm{3}×\mathrm{6}×\mathrm{8} \\ $$$$\left({xyz}\right)^{\mathrm{2}} =\mathrm{3}×\mathrm{6}×\mathrm{8}=\mathrm{12}^{\mathrm{2}} \\ $$$$\Rightarrow{xyz}=−\mathrm{12} \\ $$

Commented by HongKing last updated on 17/Dec/21

thank you dear Sir cool

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{Sir}\:\mathrm{cool} \\ $$

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