If $ a^4 +  b^4 + a^2 b^2 = 133$ and $ a^2 + b^2 - ab = 19 $, then the value of ab will be :

-6

We know that,

a⁴ + b⁴ + a²b² = (a² + b² – ab)(a² + b² + ab)

According to the question,

a⁴ + b⁴ + a²b² = 133

(a² + b² – ab)(a² + b² + ab) = 133

= 19 × (a² + b² + ab) = 133

= a² + b² + ab = 7      ....(1)

And, a² + b² – ab = 19    ....(2)

Subtract equation (2) from equation (1), we get,

2ab = -12

= ab = -6