Given, p and q are positive numbers. p+q=2 . . . (i) p4+q4=272 ⇒‌‌(p2+q2)2−2p2q2=272 ⇒‌‌[(p+q)2−2pq]2−2p2q2=272 ⇒‌‌[(2)2−2pq]2−2p2q2=272 [from Eq. (i)] ⇒‌‌(4−2pq)2−2p2q2=272 ⇒16+4p2q2−16pq−2p2q2=272 ⇒‌‌2p2q2−16pq−256=0 ⇒‌‌p2q2−8pq−128=0 pq=‌
8±√64+4×128
2×1
=‌
8±√576
2
=‌
8±24
2
∴‌‌pq=16,−8 Here, pq=−8 is not possible as p and q are positive. ∴‌‌pq=16 Now, the equation whose roots are p and q is x2−(p+q)x+pq=0 x2−2x+16=0