If a2 + b2 = 25, x2 + y2 = 17, ax + by = 8, 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

⇒ (25) (17) = 8² + n²

⇒ (25 × 17) - 64 = n²

⇒ n² =425 - 64 = 361

⇒ n = \(\sqrt {361}\) = 19