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# If x, y, and z are positive

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

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:

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

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
#2
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Very nice, mobro   !!!!   Nov 14, 2020
#3
+1

Good job, mobro! How can we find the value of x, y, and z?

Nov 14, 2020
#4
+3

Can you clarify on your question? Do you mean solving each value seprately? If so, can you ask it in a seperate question so no one gets confused? I'll try to answer it.

mobro  Nov 15, 2020
#5
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I think the question is pretty clear.

It is asking for the product.   Thanks for your answer Mobro Melody  Nov 15, 2020
edited by Melody  Nov 15, 2020