A Nice Mathematics algebra problem | Olympiad Question | Exponential problem | x=?

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[@HuzaifaKhan-m3i]

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[@AfsarSaid-f8s]

Good question

[@NaeemKhan-q6w1v]

Good

[@SrisailamNavuluri]

1040=16(65)=2^4(81-16)=2^4(3^4-2^4)=6^4-4^2
9+1/x=6,1/x=-3,x=-1/3
7+1/x=4,1/x=-3,x=-1/3.

[@SidneiMV]

8 + 1/x = u
(u + 1)⁴ - (u - 1)⁴ = 1040
u⁴ + 4u³ + 6u² + 4u + 1
- (u⁴ - 4u³ + 6u² - 4u + 1) = 1040
8u³ + 8u - 1040 = 0
u³ + u - 130 = 0
u³ - 125 + u - 5 = 0
(u - 5)(u² + 5u + 25) + (u - 5) = 0
(u - 5)(u² + 5u + 26) = 0
u = 5
8 + 1/x = 5
*x = -1/3*

[@RealQinnMalloryu4]

(3^2+/x)^2^2 ➖ (3^4+/x)2^2 (1^1+/x)^1^1 ➖ (3^2^2+/x)^1^1 (3^1^2+/x)^1 (3^2+/x) (x ➖ 3x+2).

[@Ismailorakzai-u1m]

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