Let the two numbers be x and y. Then, x+y=11 ...(i) andx2+y2=65 ...(ii) Now, on squaring Eq. (i) both sides, we get (x+y)2=121 ⇒ x2+y2+2xy=121 ⇒ x2+y2=121−2xy ⇒ x2+y2=121−2×xy ⇒ 65=121−2xy ⇒ 2xy=121−65 ⇒ 2xy=56 ⇒ xy=28 ...(iii) Now, we know that, x3+y3=(x+y)(x2+y2−xy) From Eqs. (ii) and (iii), we get ⇒ x3+y3=11×(65−28) x3+y3=11×37 ∴ x3+y3=407