Triangular OperationPro Problems > Math > Number and Quantity > Number Theory > Star Operations
SolutionIn order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
If the operation ♦ is defined as follows: a ♦ b = a2 - b2 , and 18 ♦ (x ♦ 8) = 6 ♦ 1, find all possible values of x.
x ♦ 2x = 2x ♦ x.
Note that this operation is not commutative; the order of operands cannot be exchanged without altering the result of the operation.
There exists a star (*) operation for which the following equations are true:
2 * 3 = 10
5 * 2 = 35
3 * 6 = 27
8 * 7 = 120
Find a star operation rule which satisfies all of these equations, and then use your rule to calculate the following:
10 * 11 = ?
If a * b = (a + b)2, and a # b = (a - b)2, find x such that (2 * x) # (x * 1) = 81
x * y = x2 - y2 + kx - hy. If 5 * 2 = 48 and 4 * 3 = 30, find the ordered pair (h, k).
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?