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Mathematics
Cannoli
24 July, 07:27
Solve the equation x^5-4x^4+4x^3+2x^2-5x+2=0
+4
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1
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Arias
24 July, 10:56
0
x = 2 or x = 1 or x = - 1
Step-by-step explanation:
Solve for x over the real numbers:
x^5 - 4 x^4 + 4 x^3 + 2 x^2 - 5 x + 2 = 0
The left hand side factors into a product with three terms:
(x - 2) (x - 1) ^3 (x + 1) = 0
Split into three equations:
x - 2 = 0 or (x - 1) ^3 = 0 or x + 1 = 0
Add 2 to both sides:
x = 2 or (x - 1) ^3 = 0 or x + 1 = 0
Take cube roots of both sides:
x = 2 or x - 1 = 0 or x + 1 = 0
Add 1 to both sides:
x = 2 or x = 1 or x + 1 = 0
Subtract 1 from both sides:
Answer: x = 2 or x = 1 or x = - 1
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