Question

If a² -3a+1=0 , find (i)a²+1/a² (ii)a³+1/a³ plz answer

Answer 1

a²- 3a + 1 = 0
=> a² + 1 = 3a
=> (a²+1)/a = 3
=> a + 1/a = 3

i)a² + 1/a² = (a+1/a)² - 2.a.1/a
= 3² - 2
= 9 - 2
= 7

ii) a³ + 1/a³ = (a+1/a)³ - 3.a.1/a(a+1/a)
= 3³ - 3.3
= 27 - 9
= 18

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