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For all integers m and n, where m ≠ n, m↑n = |(m^2 - n^2)/(m - n)|. Wh

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Bunuel
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For all integers m and n, where m ≠ n, m↑n = |(m^2 - n^2)/(m - n)|. Wh [#permalink] New post   14 Jan 2019, 02:43
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For all integers m and n, where m ≠ n, \(m↑n = |\frac{m^2 - n^2}{m - n}|\). What is the value of (–2)↑4?

A. 10
B. 8
C. 6
D. 2
E. 0
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D
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Re: For all integers m and n, where m ≠ n, m↑n = |(m^2 - n^2)/(m - n)|. Wh [#permalink] New post   14 Jan 2019, 02:52
Bunuel wrote:
For all integers m and n, where m ≠ n, \(m↑n = |\frac{m^2 - n^2}{m - n}|\). What is the value of (–2)↑4?

A. 10
B. 8
C. 6
D. 2
E. 0


using the expression solve for values of
we would get
2 IMO D
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Re: For all integers m and n, where m ≠ n, m↑n = |(m^2 - n^2)/(m - n)|. Wh [#permalink] New post   14 Jan 2019, 04:45
m↑n=|\(\frac{m^2−n^2}{m−n}\)|

(–2)↑4 = \(|\frac{(-2)^2 - (4)^2}{-2 - 4}|\)

= \(|\frac{4 - 16}{-6}|\)

= \(|\frac{-12}{-6}|\)

= |-2|

= 2

OPTION: D
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Re: For all integers m and n, where m ≠ n, m↑n = |(m^2 - n^2)/(m - n)|. Wh [#permalink] New post   20 Jan 2019, 08:59
simplify the modulus

|(m^2 -n^2) / (m-n)| = |(m+n)(m-n) / m-n| = |m+n| = |-2+4| = |2|
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Re: For all integers m and n, where m ≠ n, m↑n = |(m^2 - n^2)/(m - n)|. Wh [#permalink] New post   20 Jan 2019, 09:27
Bunuel wrote:
For all integers m and n, where m ≠ n, \(m↑n = |\frac{m^2 - n^2}{m - n}|\). What is the value of (–2)↑4?

A. 10
B. 8
C. 6
D. 2
E. 0


Simple expansion of \(m^2 - n^2\) = (m-n) (m+n), can help us in solving the question

\(m↑n = |\frac{m^2 - n^2}{m - n}|\)

\(m↑n = |\frac{(m-n) (m+n)}{m - n}|\)

\(m↑n = |(m+n)|\)

\(-2 ↑4 = |-2 + 4|\)

Answer D
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Re: For all integers m and n, where m ≠ n, m↑n = |(m^2 - n^2)/(m - n)|. Wh [#permalink]
20 Jan 2019, 09:27
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