If x, y, and z are positive with xy = 20, xz = 35, and yz = 14, then what is xyz?
+55 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:
\(\sqrt{9800} \implies \sqrt{4900 \cdot 2} \implies \sqrt{4900} \cdot \sqrt2 \implies \boxed{70\sqrt2}\)
+55 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:
\(\sqrt{9800} \implies \sqrt{4900 \cdot 2} \implies \sqrt{4900} \cdot \sqrt2 \implies \boxed{70\sqrt2}\)
