If $ a^4 + b^4 + a^2 b^2 = 133$ and $ a^2 + b^2 - ab = 19 $, then the value of ab will be :
Answer & explanation
Correct answer: option 2
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