If x, y, and z are positive with xy = 20, xz = 35, and yz = 14, then what is xyz?

Guest Nov 14, 2020

#1**+4 **

So we know that xy=20, xz=35, and yz=14. If we multiply them together to form an equation, we get:

\(xy \cdot xz \cdot yz = 20 \cdot 35 \cdot 14\)

Finding the product, we have:

\(x^2y^2z^2 = 9800\)

This is the same as

\((xyz)^2 = 9800\)

which finding the square root gives us

\(xyz=\sqrt{9800}\)

Simplifying, we find:

\(\sqrt{9800} \implies \sqrt{4900 \cdot 2} \implies \sqrt{4900} \cdot \sqrt2 \implies \boxed{70\sqrt2}\)

mobro Nov 14, 2020

#1**+4 **

Best Answer

So we know that xy=20, xz=35, and yz=14. If we multiply them together to form an equation, we get:

\(xy \cdot xz \cdot yz = 20 \cdot 35 \cdot 14\)

Finding the product, we have:

\(x^2y^2z^2 = 9800\)

This is the same as

\((xyz)^2 = 9800\)

which finding the square root gives us

\(xyz=\sqrt{9800}\)

Simplifying, we find:

\(\sqrt{9800} \implies \sqrt{4900 \cdot 2} \implies \sqrt{4900} \cdot \sqrt2 \implies \boxed{70\sqrt2}\)

mobro Nov 14, 2020