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If xy = 5, yz = 4, zx = 5, and z > 0, what is x3 y3 z3?
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01 Dec 2021, 02:50
01 Dec 2021, 02:50
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This question is part of the GRE - Skill Builder Project for a Q170
If xy = 5, yz = 4, zx = 5, and z > 0, what is \(x^3 y^3 z^3\)?
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1,000
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Re: If xy = 5, yz = 4, zx = 5, and z > 0, what is x3 y3 z3?
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01 Dec 2021, 07:33
01 Dec 2021, 07:33
1
Carcass wrote:
This question is part of the GRE - Skill Builder Project for a Q170
If xy = 5, yz = 4, zx = 5, and z > 0, what is \(x^3 y^3 z^3\)?
Show: ::
1,000
Given:
xy = 5
yz = 4
zx = 5
Note: If z is positive, then we can conclude that y is positive (since yz = 4), and we can conclude that x is positive (since xy = 5)
Multiply all three equations to get: (xy)(yz)(zx) = (5)(4)(5)
Simplify: x²y²z² = 100
Rewrite as: (xyz)² = 100
So, EITHER xyz = 10 OR xyz = -10
Since we've already concluded that x, y and z are all positive, it must be the case that xyz = 10
Now that we know (xyz)² = 100 and xyz = 10, we can multiply these equations to get: ((xyz)²)(xyz) = (100)(10)
Simplify: x³y³z³ = 1000
Answer: 1000
Re: If xy = 5, yz = 4, zx = 5, and z > 0, what is x3 y3 z3?
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01 Oct 2024, 01:16
01 Oct 2024, 01:16
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