If a + b = p, ab = q, then $(a^4 + b^4)$ is equal to :
Answer & explanation
Correct answer: option 4
Given,
a + b = p,
ab = q
We know that,
(a + b)2 = a2 + b2 + 2ab
So,
Squaring on both sides,
p2 = (a2 + b2) + 2q
(a2 + b2) = p2 - 2q
Then,
(a4 + b4) = (a2 + b2)2 - 2a2b2
= (p2 - 2q)2 - 2q2
= p4 - 4p2q + 2q2