If a2 + b2 = 8, x2 + y2 = 5, ax + by = 2, then find ay - bx.

Here note the result :

If ax + by = m,

and ay - bx = n

then (a² + b²)(x² + y²) = m² + n²

Therefore, using this result

⇒ (8) (5) = 2² + n²

⇒ (8 × 5) - 4 = n²

⇒ n² =40 - 4 = 36

⇒ n = \(\sqrt {36}\) = 6