Question

If p+q=2 and p^4+q^4=272 find p.q​

Answer 1

(p+q)⁴ = p⁴+q⁴+4p³q+4q³p+6p²q²

= 272+4pq(p²+q²)+6p²q²

as, p+q = 2

squaring

p²+q²+2pq = 4

p²+q² = 4-2pq

so,

(p+q)⁴ = 272+4pq(4-2pq)+6p²q²

2⁴ = 272+16pq-8p²q²+6p²q²

16 = 272+16pq-2p²q²

-256 +2p²q² = 16pq

(p²q²-128)/8 = pq ....ans.