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Star and Pound Operations

Pro Problems > Math > Number and Quantity > Number Theory > Star Operations
 

Star and Pound Operations

If a * b = (a + b)2, and a # b = (a - b)2, find x such that (2 * x) # (x * 1) = 81

 

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Problem by Mr. Twitchell

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h and k

x * y = x2 - y2 + kx - hy. If 5 * 2 = 48 and 4 * 3 = 30, find the ordered pair (h, k).

Commutative Operation

The operation * is defined as follows: x * y = (ax + b)(by + a), for some real numbers a and b. Under what conditions is this operation commutative?

 

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2 * 3 = 10
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Find a star operation rule which satisfies all of these equations, and then use your rule to calculate the following:

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Triangular Operation

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a
b
c
means a - (b x c). For example, 
20
3
4
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x
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z
y
x
z
z
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Non-Commutative Operation

If the operation a ♦ b is defined as follows: a ♦ b =
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If the operation (*) is defined as follows: a * b =
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