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If\({\rm{\;x}} + \frac{4}{{\rm{x}}} = 4,\)then find the value of x6 + 1

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If\({\rm{\;x}} + \frac{4}{{\rm{x}}} = 4,\)then find the value of x6 + 1
1). 51
2). 65
3). 78
4). 82


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1 answers

3 vote
Answered by on | Votes 3 |

Given,

x + 4/x = 4

⇒ x2 + 4 = 4x

⇒ x2 - 4x + 4 = 0

⇒ (x - 2)2 = 0

⇒ x = 2

∴ (x6 + 1) = 26 + 1 = 64 + 1 = 65

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