1) (x-2)(x^2+2x+4)-x^2(x-18) = 0Expanding the left side:(x^3 + 2x^2 + 4x - 2x^2 - 4x - 8) - (x^3 - 18x^2) = 0Simplifying:x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 - x^3 + 18x^2 = 0x^2 + 18x^2 - 2x^2 - 4x + 4x - 8 = 017x^2 - 8 = 017x^2 = 8x^2 = 8/17x = ±√(8/17)
2) x^2 - 12 = 0x^2 = 12x = ±√12 = ±2√3
Therefore, the solutions are:x = ±√(8/17), ±2√3
1) (x-2)(x^2+2x+4)-x^2(x-18) = 0
Expanding the left side:
(x^3 + 2x^2 + 4x - 2x^2 - 4x - 8) - (x^3 - 18x^2) = 0
Simplifying:
x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 - x^3 + 18x^2 = 0
x^2 + 18x^2 - 2x^2 - 4x + 4x - 8 = 0
17x^2 - 8 = 0
17x^2 = 8
x^2 = 8/17
x = ±√(8/17)
2) x^2 - 12 = 0
x^2 = 12
x = ±√12 = ±2√3
Therefore, the solutions are:
x = ±√(8/17), ±2√3