alliegreen
Answered

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x^4 + 4x^3 + 4x^2 = -16x

Sagot :

Panoyin
                      x⁴ + 4x³ + 4x² = -16x
            x⁴ + 4x³ + 4x² + 16x = -16x + 16x
            x⁴ + 4x³ + 4x² + 16x = 0
x(x³) + x(4x²) + x(4x) + x(16) = 0
           x(x³ + 4x² + 4x + 16) = 0
  x(x²(x) + x²(4) + 4(x) + 4(4)) = 0
          x(x²(x + 4) + 4(x + 4)) = 0
                    x(x² + 4)(x + 4) = 0
x = 0  U  x² + 4 = 0  U  x + 4 = 0
                   - 4  - 4          - 4  - 4
                     x² = -4          x = -4
                      x = +2i
The solution set is equal to {-4, -2i, 0, 2i}.
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