Question

If (x^2+1)/x= 5/2 Find x^3-1/x^3
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Answer 1

Answer:

63/8(improper fraction) or 7 7/8(mixed fraction) or 7.875(decimals)

Step-by-step explanation:

(x^2 + 1)/x = 5/2

=> x + 1/x = 5/2

Squaring both sides,

=> (x + 1/x)^2 = (5/2)^2

=> x^2 + 1/x^2 + 2 = 25/4

=> x^2 + 1/x^2 + 2 - 4 = 25/4 - 4

=> x^2 + 1/x^2 - 2 = 9/4

=> (x - 1/x)^2 = 9/4

taking the square root on both sides,

=> x - 1/x = +/- 3/2

Cubing both sides,

=> (x - 1/x)^3 = (+/- 3/2)^3

=> x^3 - 1/x^3 - 3.x.1/x.(x-1/x) = +/- 27/8

=> x^3 - 1/x^3 - 3(+/- 3/2) = +/- 27/8

=> x^3 - 1/x^3 - (+/- 9/2) = +/- 27/8

=> x^3 - 1/x^3 = +/- 27/8  + (+/- 9/2)

=> x^3 - 1/x^3 = +/- (27/8  + 9/2)

=> x^3 - 1/x^3 = +/- 63/8   ... (answer)

Therefore, answer is 63/8(improper fraction) or 7 7/8(mixed fraction) or 7.875(decimals).