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# help

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

Dec 10, 2019

#1
+8806
+1

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

Hello bigmac!

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

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

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

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

!

Dec 11, 2019