Question

5. If 2(x^2 + 1) = 5x, find :
(1) x-1/x
(2) x^3 -1/x^3

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Answer 1

x^2+2=5x

2x^2-5x+2=0

2x^2-4x-x+2=0

2x(x-2)-1(x-2)=0

(x-2)(2x-1)=0

x-2=0 or 2x-1=0

x=2 or x=1/2

therefore

if x=2

x-1/x =2-1/2=3/2

if x=1/2

x-1/x =1/2-2

=-3/2