Answer :
x⁶ - 64 = 0
x⁶ + 8x³ - 8x³ - 64
(x³ - 8)(x³ + 8) = 0
x³ - 8 = 0 or x³ + 8 = 0
+8 +8 -8 -8
x³ = 8 x³ = -8
x = 2 x = 2i
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36x⁸ - 13x⁴ + 1 = 0
36x⁸ - 9x⁴ - 4x⁴ + 1 = 0
(9x⁴ - 1)(4x⁴ - 1) = 0
9x⁴ - 1 = 0 or 4x⁴ - 1 = 0
+1 +1 +1 +1
9x⁴ = 1 4x⁴ = 1
9 9 4 4
x⁴ ≈ 0.1 x⁴ = 0.25
x ≈ 0.6 x ≈ 0.71
x⁶ + 8x³ - 8x³ - 64
(x³ - 8)(x³ + 8) = 0
x³ - 8 = 0 or x³ + 8 = 0
+8 +8 -8 -8
x³ = 8 x³ = -8
x = 2 x = 2i
-----------------------------------------------------------------------------------------------
36x⁸ - 13x⁴ + 1 = 0
36x⁸ - 9x⁴ - 4x⁴ + 1 = 0
(9x⁴ - 1)(4x⁴ - 1) = 0
9x⁴ - 1 = 0 or 4x⁴ - 1 = 0
+1 +1 +1 +1
9x⁴ = 1 4x⁴ = 1
9 9 4 4
x⁴ ≈ 0.1 x⁴ = 0.25
x ≈ 0.6 x ≈ 0.71
