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If a, b, and c are consecutive integers, where a < b < c, which of the
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Bunuel
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If a, b, and c are consecutive integers, where a < b < c, which of the [#permalink] New post  26 Jan 2021, 02:15
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If a, b, and c are consecutive integers, where \(a < b < c\), which of the following cannot be the value of \(c^2 - (a^2 + b^2)\)?

A. -21
B. -12
C. -6
D. 0
E. 3


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a,b and c are consecutive integers where a<b<c. which of the following could not be the value of c^2-b^2-a^2?
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If a, b, and c are consecutive integers, where a < b < c, which of the [#permalink] New post  26 Jan 2021, 04:13
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Bunuel wrote:
If a, b, and c are consecutive integers, where \(a < b < c\), which of the following cannot be the value of \(c^2 - (a^2 + b^2)\)?

A. -21
B. -12
C. -6
D. 0
E. 3


Show Spoiler
a,b and c are consecutive integers where a<b<c. which of the following could not be the value of c^2-b^2-a^2?


if a = x-1, then b = x and c = x+1

\(c^2 - (a^2 + b^2) = (x+1)^2 - [x^2+(x-1)^2] = x^2+1+2x - x^2 - x^2 - 1 +2x = -x^2 +4x = x(4-x)\)

A. -21 = (-3)*(4-(-3)) hence POSSIBLE
B. -12 = (-2)*(4-(-2)) hence POSSIBLE
C. -6 ≠ (-1)*(4-(-1)) hence NOT POSSIBLE
D. 0 = (0)*(4-(0)) hence POSSIBLE
E. 3 = (1)*(4-(1)) hence POSSIBLE

ANswer: Option C
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