Question

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

Answer 1

Answer:

1. -1 or 1/2

2. -7 or 7/8

Step-by-step explanation:

2(x^2+1) = 5x

2x^2+2=5x

2x^2-5x+2=0

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

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

x== 1/2 or 2

(1) x-1/x

If x = 1/2

= 1/2-1/1/2

= -1/2/1/2

=-1

If x = +2

2-1/2

= 1/2

(2) x^3-1/x^3

If x = 1/2

(1/2)^3-1/(1/2)^3

= 1/8-1/1/8

= -7

If x = 2

= (2)^3-1/(2)^3

= 8-1/8

= 7/8