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Asked by Neha Vilasi

Aug 19, 2013

If x + 1/x = 3 , then find the value of x6+1/x6.

If x +1 =3 , then find the value of x6+1.

        x                                                 x6

Answers(4)

Answer

Syeda

Member since Jan 25, 2017

x+1/x =3
1/x     =3-x
1        = 3-x2
1-3     = -x2
-2       = -x2
√2      = x
x+1/x  = √26+1/√26
          = 2*2*2+1/2*2*2
          = 8+1/8 ⇒ 8/1+1/8  LCM= 8 
          = 64/8+1/8
          = 65/8
             or
          = 8.125

Vaikuntha vaasan

Member since

x+1/x =3
1/x     =3-x
1        = 3-x2
1-3     = -x2
-2       = -x2
√2      = x
x+1/x  = √26+1/√26
          = 2*2*2+1/2*2*2
          = 8+1/8 ⇒ 8/1+1/8  LCM= 8 
          = 64/8+1/8
          = 65/8
             or
          = 8.125

Sanjay Bharadwaj

Member since

give the question properly

Kishore Kumar

Member since

Assuming the question as (x + 1/x) = 3
Squaring on both the sides we get
(x + 1/x)2 = 32
x2 +(1/x2) + 2 = 9
⇒ x2 +(1/x2)  = 7
Now cubing on both the sides we get,
[x2 +(1/x2)]3  = 73
LHs is in the form of (a + b)3 = a3 + b3 + 3ab (a + b)
Hence [x2]3 + [(1/x2)]3 + 3 (x2) × (1/x2)[x2 +(1/x2)]  = 343
⇒ x6 + (1/x6) + 3 × 7 = 343
⇒ x6 + (1/x6) + 21 = 343
∴  x6 + (1/x6)  = 343 − 21 = 322


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