Verified answer

(x+1/x)²-5(x+1/x)+6=0

x+1/x = 2 ou x+1/x = 3

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x+1/x=2

x²-2x +1 =0

x=1

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x+1/x=3

x²-3x+1 =0

delta = 9-4 = 5

raizdelta = √5

x =(3+√5)/2

x =(3-√5)/2

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S = (1, (3+√5)/2, (3-√5)/2)

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y = (x + 1/x)

y² - 5y + 6 = 0

(y - 3)*(y - 2) = 0

y1 = 3

y2 = 2

x + 1/x = 3

x² - 3x + 1 = 0

d² = 9 - 4 = 5

x1 = (3 + √5)/2

x2 = (3 - √5)/2

x + 1/x = 2

x² - 2x + 1 = 0

(x - 1)² = 0

x = 1

pronto