Question

х^4-71х^2+270х-200=0
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Answer 1

$x {}^{4} - 71x {}^{2} + 270x - 200 = 0 \\ x {}^{4} - x {}^{3} + x {}^{3} - x^{2} - 70x {}^{2} + 70x + 200x - 200 = 0 \\ x {}^{3} (x - 1) + x {}^{2} (x - 1) - 70x(x - 1) + 200(x - 1) = 0 \\ (x - 1)(x {}^{3} + x {}^{2} - 70x + 200) = 0 \\ (x - 1)(x {}^{3} - 4x {}^{2} + 5x {}^{2} - 20x - 50x + 200) = 0 \\ (x - 1)(x {}^{2} \times (x - 4) + 5x(x - 4) - 50(x - 4)) = 0 \\ (x - 1)(x - 4)(x {}^{2} + 5x - 50) = 0 \\ (x - 1)(x -4)(x {}^{2} + 10x - 5x - 50) = 0 \\ (x - 1)(x - 4)(x(x + 10) - 5(x + 10)) = 0 \\ (x - 1)(x - 4)(x + 10)(x - 5) = 0 \\ x - 1 = 0 \\ x - 4 = 0 \\ x + 10 = 0 \\ x - 5 = 0 \\ x _{1} = 1 \\ x _{2} = 4 \\ x _{3} = - 10 \\ x _{4} = 5$