Master Algebra in Minutes with These 2 Unique Methods!

[@wes9627]

Let b=a^{5/2} so (b+1/b)^2-2=724. Thus, b+1/b=√726 (b+1/b)(b^2+1/b^2)=b^3+1/b^3+(b+1/b)=b^3+1/b^3+√726=724*√726 This yields b^3+1/b^3=a^7√a+1/(a^7√a)=√726*723=7953√6

[@潘博宇-k4l]

E=7953(6)^(1/2)

[@Shobhamaths]

E=7953√6👍

[@ShriH-d1o]

Let {(a^2)√a+1/(a^2)√a)}=x & y=a^5+1/a^5; => x^2=y+2=724 +2=726;, x=√726=11√6; also {(a^7)√a+1/a^7√a}= (x)(y)-x =724(11√6)-11√6= (724-1)11√6=723(11√6)

[@Quest3669]

?= (√726)^3-3√726= √726× 723= 11√6×723= 7953√6 soln.