Question

ifx^2-3x+1=0 find the value of (x^3+1/x^3)​

Answer 1

Answer:

Step-by-step explanation:

Given, x2 – 3x + 1 = 0

→ x2 + 1 = 3x

→ x + 1/x = 3   (Dividing both sides by x)

→ x2 + 1/x2 + 2 = 9

→ x2 + 1/x2 = 7     ----(1)

→ x2 + 1/x2 – 2 = 5

→ (x – 1/x)2 = 5

→ x – 1/x = (5)1/2   ---(2)

 

Now, x3 + 1/x3

= (x - 1/x)(x2 + 1/x2 + 1)

= 51/2 * (7 +1)

= 8 * 51/2

= 8√5

Answer 2

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