Question

If ⊕ ÷ ⊙ = 2; 

⊕ ÷ Δ = 3; 

⊙ + Δ = 5; 

Δ × ⊗ = 10,

Then the value of (⊗ - ⊕)², is 

Answer 1

Correct Answer - Option 2 : 1

Explanation:

Given:

⊕ ÷ ⊙ = 2, Δ × ⊗ = 10, ⊙ + Δ = 5; Δ × ⊗ = 10

∵ \(\frac{⊕}{⊙} = 2\), \(\frac{⊕}{Δ} = 3\)

∴ \(\frac{⊙ }{Δ}=\frac{3}{2}\) 

\(⊙=\frac{3Δ}{2}\)

now, ⊙ + Δ = 5 

\(\frac{3Δ}{2} + Δ = 5 \)

5Δ = 10

∴ Δ = 2

∵ ⊙ + 2 = 5 

∴ ⊙ = 3

Now,  Δ × ⊗ = 10

2 × ⊗ = 10

∴ ⊗ = 5

Now, \(\frac{⊕}{⊙} = 2\)

\(\frac{⊕}{3} = 2\)

∴ ⊕ = 6

Hence (⊗ - ⊕)2 = (5 - 6)² = 1