x + 1/x = 1 হলে (x2+ 1/x2)(x4+ 1/x4) = ?

x + 1/x = 1
বা, (x + 1/x)² = 1
বা, x² + 2.x.1/x + 1/x² = 1
x² + 1/x² + 2 = 1
বা, x² + 1/x² = -1
বা, (x² + 1/x²)² = 1
x⁴ + 2.x².1/x² + 1/x⁴ = 1
বা, x⁴ + 1/x⁴ + 2 = 1
∴ x⁴ + 1/x⁴ = -1
∴ (x² + 1/x²)(x⁴ + 1/x⁴) = (-1)(-1)
= 1