Diamond Operation
Pro Problems > Math > Number and Quantity > Number Theory > Star OperationsDiamond Operation
If the operation ♦ is defined as follows: a ♦ b = a2 - b2 , and 
18 ♦ (x ♦ 8) = 6 ♦ 1, find all possible values of x.
Solution
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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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h and k
x * y = x2 - y2 + kx - hy. If 5 * 2 = 48 and 4 * 3 = 30, find the ordered pair (h, k).
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