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Given 3 3 = 5 and 6 4 = 20, what is the rule for a b?

Mathematics

ScanSolve AI Answer

The problem defines a custom mathematical operator Ψ\Psi using two examples:

  1. 3Ψ3=53 \Psi 3 = 5
  2. 6Ψ4=206 \Psi 4 = 20

We need to find a rule aΨb=f(a,b)a \Psi b = f(a, b) that satisfies both examples.

Let's test a common pattern for such problems: aΨb=(a×b)−Ca \Psi b = (a \times b) - C.
Using the first example:
3Ψ3=(3×3)−C=53 \Psi 3 = (3 \times 3) - C = 5
9−C=59 - C = 5
C=9−5C = 9 - 5
C=4C = 4
So, the rule could be $a \Psi b = (a \times b

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