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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

Syeda

Member since Jan 25, 2017

x+1/x =3 1/x     =3-x 1        = 3-x2 1-3     = -x2 -2       = -x2 âˆš2      = x x+1/x  = âˆš26+1/âˆš26           = 2*2*2+1/2*2*2           = 8+1/8 â‡’ 8/1+1/8  LCM= 8            = 64/8+1/8           = 65/8              or           = 8.125 SME Approved

Vaikuntha vaasan

Member since

x+1/x =3 1/x     =3-x 1        = 3-x2 1-3     = -x2 -2       = -x2 âˆš2      = x x+1/x  = âˆš26+1/âˆš26           = 2*2*2+1/2*2*2           = 8+1/8 â‡’ 8/1+1/8  LCM= 8            = 64/8+1/8           = 65/8              or           = 8.125

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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 â‡’ 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) Ã— (1/x2)[x2 +(1/x2)]  = 343 â‡’ x6 + (1/x6) + 3 Ã— 7 = 343 â‡’ x6 + (1/x6) + 21 = 343 âˆ´  x6 + (1/x6)  = 343 âˆ’ 21 = 322
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