Composing an Operation

Algebra Level 1

The operation ⊗ \otimes is defined as a ⊗ b = a 2 + b 2 a \otimes b = a^2 + b^2 . What is the value of ( 1 ⊗ 2 ) ⊗ 3 (1\otimes 2) \otimes 3 ?


The answer is 34.

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Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

( 1 ⊗ 2 ) ⊗ 3 = ( 1 2 + 2 2 ) ⊗ 3 = 5 ⊗ 3 = 5 2 + 3 2 = 25 + 9 = 34. (1\otimes 2) \otimes 3 = (1^2 + 2^2) \otimes 3 = 5 \otimes 3 = 5^2 + 3^2 = 25 + 9 = 34.

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