Question

solve for 'x'

${x}^{4} - 2 {x}^{3} + x = 380$

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Answer 1

✌HEYA YOUR ANSWER IS ABOVE ✌

Answer 2

Step-by-step explanation:

Given Equation is x⁴ - 2x³ + x = 380

⇒ x⁴ - 2x³ + x - 380 = 0

⇒ x⁴ - 6x³ + 4x³ + 24x² - 24x² - 95x + 96x - 380 = 0

⇒ x⁴ - 6x³ + 24x² - 95x + 4x³ - 24x² + 96x - 380 = 0

⇒ x(x³ - 6x² + 24x - 95) + 4(x³ - 6x² + 24x - 95) = 0

⇒ (x + 4)(x³ - 6x² + 24x - 95) = 0

⇒ (x + 4)(x - 5)(x² - x + 19) = 0

(i)

x = -4

(ii)

x = 5

(iii)

x² - x + 19 = 0

∴ x = (-b ± √b² - 4ac)/2a

⇒ (1 ± √75)i/2

⇒ (1/2) ± (√75)/2 i

⇒ (1/2) ± (5√3/2) i

∴ x = -4,  5,   (1/2) + i(5√3/2),  (1/2) - i(5√3/2)

Hope it helps!