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if x^2-3x+1=0 then the value of x^3-1/x^3 is where x cannot be equal to 0

if x^2-3x+1=0 then the value of x^3-1/x^3 is where x cannot be equal to 0

Grade:12th pass

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
6 years ago
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Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your question.
 
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
 
Hope it helps,
Thanks and regards,
Kushagra
 

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