Question

⊗ and ⊙ are two operators on numbers p and q such that \(p \oplus q=\frac{p^2+q^2}{pq}\) and \(p \odot q =\frac{p^2}{q};\) If x ⊕ y = 2 ⊙ 2, then, x = 
1. y/2
2. y
3. \(\frac{3y}{2}\)
4. 2y

Answer 1

Correct Answer - Option 2 : y

Given:

\(p \oplus q=\frac{p^2+q^2}{pq}\)

\(p \odot q =\frac{p^2}{q};\)

Calculation:

LHS = x ⊕ y = \(\frac{x^2+y^2}{xy}\)

RHS = 2 ⊙ 2 = 2²/2 = 2

⇒ 2 ⊙ 2 = 2

\(\frac{x^2+y^2}{xy} = 2\)

⇒ x² + y² = 2xy

⇒ x2 + y2 – 2xy = 0

⇒ (x – y)² = 0

Thus,

x = y