If x+1/x=2 and x is real, then the value of x^17+1/x^19 is:

Algebra and Applications Test 2

Question : 15 of 40

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x+1/x=2

and x is real, then the value of

x^17+1/x^19

is:

Solution:

x+1/x=2

x^2 + 1 = 2x

x^2 - 2x + 1 = 0

x^2 - x - x + 1 = 0

x (x - 1) - 1(x - 1) = 0

(x - 1) (x - 1) = 0

x = 1, 1

∴ x^17+1/x^19=2

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