⊕ and ⊗ are two operators on numbers p and q such that p ⊕ q = (p^2 + q^2)/(pq) and p ⊗ q = p^2/q^2. If z = p ⊗ q, then ...

Question

⊕ and ⊗ are two operators on numbers p and q such that p ⊕ q = (p^2 + q^2)/(pq) and p ⊗ q = p^2/q^2. If z = p ⊗ q, then z =

A. p^2/q^2  B. p/q  C. p^2/q  D. 2q

Accepted Answer

z = p^2/q^2 (Option A). Two custom binary operators ⊕ and ⊗ are defined on real numbers p and q. The operator ⊗ is a squaring-ratio operator: it squares both p and q and takes their ratio. The question asks what z equals when z is defined as p ⊗ q — this checks whether the student can correctly apply the operator definition without algebraic manipulation errors.