1) x^3 - 169 = 0x^3 = 169x = ∛169x = 5
2) x^4 - 4x^2 - 32 = 0Let y = x^2y^2 - 4y - 32 = 0(y - 8)(y + 4) = 0y = 8 or y = -4
If y = 8:x^2 = 8x = ±√8x = ±2√2
If y = -4:x^2 = -4This has no real solutions
Therefore, the solutions are x = 2√2 and x = -2√2.
1) x^3 - 169 = 0
x^3 = 169
x = ∛169
x = 5
2) x^4 - 4x^2 - 32 = 0
Let y = x^2
y^2 - 4y - 32 = 0
(y - 8)(y + 4) = 0
y = 8 or y = -4
If y = 8:
x^2 = 8
x = ±√8
x = ±2√2
If y = -4:
x^2 = -4
This has no real solutions
Therefore, the solutions are x = 2√2 and x = -2√2.