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555-605 Level|   Algebra|      
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Bunuel
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If (4 - 2y)/(2 + y) = y, what is the value of y^2 + 4y + 4? 21 Aug 2019, 00:51
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E
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Difficulty:

35% (medium)

Question Stats:

65% (01:24) correct 35% (02:09) wrong based on 68 sessions

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If \(\frac{4 - 2y}{2 + y} = y\), what is the value of \(y^2 + 4y + 4\)?

A. -4
B. -1
C. 0
D. 1
E. 8
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E
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If (4 - 2y)/(2 + y) = y, what is the value of y^2 + 4y + 4? 21 Aug 2019, 00:57
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Y^2+2Y=4-2Y
Y^2+4Y=4
So,Y^2+4Y+4=4+4=8
Option E

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If (4 - 2y)/(2 + y) = y, what is the value of y^2 + 4y + 4? 21 Aug 2019, 00:59
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4-2y = 2y+ y^2
Rearranging
y^2+4y = 4
Therefore
y^2 + 4y + 4 = 4+4 = 8
Hence IMO E is the answer.

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If (4 - 2y)/(2 + y) = y, what is the value of y^2 + 4y + 4? 21 Aug 2019, 01:02
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Bunuel
If \(\frac{4 - 2y}{2 + y} = y\), what is the value of \(y^2 + 4y + 4\)?

A. -4
B. -1
C. 0
D. 1
E. 8

Given: \(\frac{4 - 2y}{2 + y} = y\)

Asked: What is the value of \(y^2 + 4y + 4\)?

\(\frac{4 - 2y}{2 + y} = y\)
\(\frac{4 - 2y}{2 + y} -y = 0\)
\(\frac{(4 - 2y)-(2y + y^2)}{(2 + y)y} = 0\)
\(\frac{(4 - 4y - y^2)}{(2 + y)y} = 0\)
\(y \neq 0\) and \(y \neq -2\)
\(4 - 4y - y^2 = 0\)
\(y^2 + 4y = 4\)
\(y^2 + 4y + 4 = 8\)

IMO E
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