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14 Aug 2024, 01:30
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Difficulty:
25%
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Question Stats:
84% (01:57) correct
16%
(02:13)
wrong
based on 134
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Both x and y are positive integers. If \(x^2 + 2xy + y^2 = 49\) and \(x^2 − y^2 = −7\), then \(y = \)
A. 2
B. 3
C. 4
D. 5
E. 7
A. 2
B. 3
C. 4
D. 5
E. 7
\(x^2+2xy+y^2=49\\
(x+y)^2=49\\
x+y=7\\
x^2−y^2=−7\\
(x+y)(x-y)=-7\\
(7)(x-y)=-7\\
(x-y)=\frac{-7}{7}\\
x-y=-1\\
x=y-1\\
(y-1)+y=7\\
2y-1=7\\
2y=7+1\\
2y=8\\
y=4\)
Option C
(x+y)^2=49\\
x+y=7\\
x^2−y^2=−7\\
(x+y)(x-y)=-7\\
(7)(x-y)=-7\\
(x-y)=\frac{-7}{7}\\
x-y=-1\\
x=y-1\\
(y-1)+y=7\\
2y-1=7\\
2y=7+1\\
2y=8\\
y=4\)
Option C
14 Aug 2024, 07:11
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cryuss
Correct highlighted part.
