Question-61537

Question Number 61537 by aanur last updated on 04/Jun/19

Commented by aanur last updated on 04/Jun/19

$${sir}\:{could}\:{you}\:{help}\:{me} \\ $$

Commented by math1967 last updated on 04/Jun/19

xyz×(√(x^2 ×y^2 ×z^2 )) =4×9×16 x^2 ×y^2 ×z^2 =4×9×16⇒xyz=2×3×4

$${xyz}×\sqrt{{x}^{\mathrm{2}} ×{y}^{\mathrm{2}} ×{z}^{\mathrm{2}} }\:=\mathrm{4}×\mathrm{9}×\mathrm{16} \\ $$$${x}^{\mathrm{2}} ×{y}^{\mathrm{2}} ×{z}^{\mathrm{2}} =\mathrm{4}×\mathrm{9}×\mathrm{16}\Rightarrow{xyz}=\mathrm{2}×\mathrm{3}×\mathrm{4} \\ $$

Answered by MJS last updated on 04/Jun/19

(1) ⇒ z=((16)/(x^2 y)) (2) ((4(√y))/( (√x)))=9 (3) ((16)/( (√(x^3 y))))=16 (2) ⇒ y=((81x)/(16)) ⇒ z=((256)/(81x^3 )) (3) ((64)/(9x^2 ))=16 ⇒ x=(2/3) ⇒ y=((27)/8) ∧ z=((32)/3)

$$\left(\mathrm{1}\right)\:\Rightarrow\:{z}=\frac{\mathrm{16}}{{x}^{\mathrm{2}} {y}} \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{4}\sqrt{{y}}}{\:\sqrt{{x}}}=\mathrm{9} \\ $$$$\left(\mathrm{3}\right)\:\frac{\mathrm{16}}{\:\sqrt{{x}^{\mathrm{3}} {y}}}=\mathrm{16} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\Rightarrow\:{y}=\frac{\mathrm{81}{x}}{\mathrm{16}}\:\Rightarrow\:{z}=\frac{\mathrm{256}}{\mathrm{81}{x}^{\mathrm{3}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{\mathrm{64}}{\mathrm{9}{x}^{\mathrm{2}} }=\mathrm{16}\:\Rightarrow\:{x}=\frac{\mathrm{2}}{\mathrm{3}}\:\Rightarrow\:{y}=\frac{\mathrm{27}}{\mathrm{8}}\:\wedge\:{z}=\frac{\mathrm{32}}{\mathrm{3}} \\ $$

Answered by Kunal12588 last updated on 04/Jun/19

i) x(√(yz))=4 ii) y(√(xz))=9 iii) z(√(xy))=16 i×ii×iii ⇒xyz(√(x^2 y^2 z^2 ))=2^6 ×3^2 ⇒(xyz)^2 =2^6 ×3^2 ⇒xyz=2^3 ×3=24 (i)^2 ⇒x^2 yz=4^2 =16 ⇒((x^2 yz)/(xyz))=((16)/(24)) ⇒x=(2/3) (ii)^2 ⇒xy^2 z=81 ⇒y=((81)/(24))=((27)/8) (iii)^2 ⇒xyz^2 =256 ⇒z=((256)/(24))=((32)/3)

$$\left.{i}\right)\:{x}\sqrt{{yz}}=\mathrm{4} \\ $$$$\left.{ii}\right)\:{y}\sqrt{{xz}}=\mathrm{9} \\ $$$$\left.{iii}\right)\:{z}\sqrt{{xy}}=\mathrm{16} \\ $$$${i}×{ii}×{iii} \\ $$$$\Rightarrow{xyz}\sqrt{{x}^{\mathrm{2}} {y}^{\mathrm{2}} {z}^{\mathrm{2}} }=\mathrm{2}^{\mathrm{6}} ×\mathrm{3}^{\mathrm{2}} \\ $$$$\Rightarrow\left({xyz}\right)^{\mathrm{2}} =\mathrm{2}^{\mathrm{6}} ×\mathrm{3}^{\mathrm{2}} \\ $$$$\Rightarrow{xyz}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3}=\mathrm{24} \\ $$$$\left({i}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{x}^{\mathrm{2}} {yz}=\mathrm{4}^{\mathrm{2}} =\mathrm{16} \\ $$$$\Rightarrow\frac{{x}^{\mathrm{2}} {yz}}{{xyz}}=\frac{\mathrm{16}}{\mathrm{24}} \\ $$$$\Rightarrow{x}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left({ii}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{xy}^{\mathrm{2}} {z}=\mathrm{81} \\ $$$$\Rightarrow{y}=\frac{\mathrm{81}}{\mathrm{24}}=\frac{\mathrm{27}}{\mathrm{8}} \\ $$$$\left({iii}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{xyz}^{\mathrm{2}} =\mathrm{256} \\ $$$$\Rightarrow{z}=\frac{\mathrm{256}}{\mathrm{24}}=\frac{\mathrm{32}}{\mathrm{3}} \\ $$

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