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If xy = 24, xz = 30, and yz = 15, then find x + y + z.

 Dec 10, 2019
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If xy = 24, xz = 30, and yz = 15, then find x + y + z.

 

Hello bigmac!

 

\(x=\frac{24}{y}\ ;\ \ x=\frac{30}{z}\\ y=\frac{24}{x}\ ;\ \ y=\frac{15}{z}\\ z=\frac{30}{x}\ ;\ \ z=\frac{15}{y}\)

 

\(x=2y\\ xy=24\\ 2y^2=24\\ \color{blue}y=\sqrt{12}\\ \color{blue}y=2\sqrt{3}\\ \color{blue}x=4\sqrt{3}\)

 

\(z=\frac{15}{y}=\frac{15}{2\sqrt{3}}=\frac{\sqrt{3}\cdot 5}{2}\\ \color{blue}z=\frac{\sqrt{3}\cdot 5}{2}\)

 

\(x+y+z=4\sqrt{3}+2\sqrt{3}+\frac{5\sqrt{3}}{2}=\sqrt{3}\cdot \frac{17}{2}\)

 

laugh  !

 Dec 11, 2019

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