If m=(2-√3),then the value of (m6+m4+m2+1) /m3 is:

• given, (m⁶ + m⁴ + m² + 1)/m³
  (m⁶/m³ + m⁴/m³ + m²/m³ + 1/m³)
  (m³ + m + 1/m + 1/m³)
  now,
  m = (2 - √3)------------( 1 )
  m³ = (8 - 3√3 - 6√3(2 - √3)
  m³ = (8 - 3√3 - 12√3 + 18)
  m³ = (26 - 15√3)-----------( 2 )
  1/m = 1/(2 - √3) * (2 + √3)/(2 + √3)
  1/m = (2 + √3)/(4 - 3)
  1/m = (2 + √3)------------( 3 )
  1/m³ = 1/(26 - 15√3) * (26 + 15√3)/(26 + 15√3)
  1/m³ = (26 + 15√3)/(676 - 675)
  1/m³ = (26 + 15√3)-------------( 4 )
  adding------( 1 ) , --------( 2 ) , --------( 3 ) & --------( 4 )
  (m + 1/m + m³ + 1/m³)
  = (2 - √3 + 2 + √3 + 26 - 15√3 + 26 + 15√3)
  = (4 + 52)
  = 56
  Hence, (m⁶ + m⁴ + m² + 1)/m³ = 56
• 5 years agoHelpfull: Yes(1) No(0)