If x² + x = 11
find (x+4)³ +1/((x+4)³)
Let x+4 = m x = m – 4 Now, x² + x = 11 (m – 4)² + m – 4 = 11 m² + 16 - 8m + m – 4 – 11 = 0 m² + 1 - 7m = 0 m² + 1 = 7m Dividing the equation by m We get, m + 1/m = 7 m³ + 1/m³ = (m + 1/m)³ - 3(m + 1/m) = 343 – 21 = 322
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