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If x 0 and x = (4xy - 4y^2)^(1/2), then in terms of y, x = ?
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07 May 2022, 00:35
07 May 2022, 00:35
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Question Stats:
91% (01:18) correct
8% (00:48) wrong based on 12 sessions
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If \(x ≠ 0\) and \(x = \sqrt{4xy - 4 y^2}\), then in terms of y, x = ?
A. \(2y\)
B. \(y\)
C. \(\frac{y}{2}\)
D. \(\frac{4y^2}{1-4y}\)
E. \(-2y\)
A. \(2y\)
B. \(y\)
C. \(\frac{y}{2}\)
D. \(\frac{4y^2}{1-4y}\)
E. \(-2y\)
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Re: If x 0 and x = (4xy - 4y^2)^(1/2), then in terms of y, x = ?
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07 May 2022, 05:13
07 May 2022, 05:13
1
Carcass wrote:
If \(x ≠ 0\) and \(x = \sqrt{4xy - 4 y^2}\), then in terms of y, x = ?
A. \(2y\)
B. \(y\)
C. \(\frac{y}{2}\)
D. \(\frac{4y^2}{1-4y}\)
E. \(-2y\)
A. \(2y\)
B. \(y\)
C. \(\frac{y}{2}\)
D. \(\frac{4y^2}{1-4y}\)
E. \(-2y\)
Given: \(x = \sqrt{4xy - 4y^2}\)
Square both sides of the equation: \(x^2 = 4xy - 4y^2\)
Strategy: Since this looks like a quadratic equation, let's set it equal to 0
Add \(4y^2\) and subtract \(4xy\) to/from both sides of the equation: \(4y^2 - 4xy + x^2 = 0\)
Strategy: This looks like one of the special products \((a-b)(a-b) = a^2 - 2ab + b^2\)
Factor the left side to get: \((2y - x)(2y - x) = 0\)
At this point, we can conclude that \(2y - x = 0\), which means \(x = 2y\)
Answer: A
Re: If x 0 and x = (4xy - 4y^2)^(1/2), then in terms of y, x = ?
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17 Feb 2024, 13:53
17 Feb 2024, 13:53
Hello Brent, for this we're not expected to check for extraneous root?
