If ax + by = 6, bx – ay = 2 and x 2 + y 2 = 4, then the value of ( a 2 + b 2) would be :

As we know that given in question,
ax + by = 6 ........................ (i)
bx – ay = 2 ........................ (ii)
On squaring the both equation and adding,
a² x² + b² y² + 2abxy + b² x² + a² y² – 2abxy = 36 + 4
⇒ x² (a² + b²) + y² (a² + b²) = 40
⇒ (a² + b²) (x² + y²) = 40
As per given question, x² + y² = 40 , Put this value in above equation, we will get
⇒ (a² + b²) × 4 = 40
⇒ a² + b² = 10