Evaluating A Nice Algebraic Expression | Three Methods

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a^2-3a+1=0
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[@alextang4688]

a^2-3a+1=0
a^2=3a-1
Use this to lessen the power of the expression and find the answer is the simplest way.
(The expression can be in any form of a's power and with different degrees.)😋😋😋😋😋😋

[@scottleung9587]

I used the second method, but the third one was brilliant!

[@SyberMath]

Excellent!

[@mcwulf25]

Easy. Rearrange the first eqn
a + 1/a = 3 (a|=0)
Cube this to get
a^3 + 1/a^3 + 3(a + 1/a) = 27
a^3 + 1/a^3 = 27-9 = 18
Square this to get
a^6 + 1/a^6 + 2 = 18^2 = 324
a^6 + 1/a^6 = 324-2 = 322

[@nicolascamargo8339]

Excelente

[@giuseppemalaguti435]

7*46

[@남이명준-s1b]

329

[@chrisjuravich3398]

322