Question

5. If 2(x2 + 1) = 5x, find :

(i) x -1/x
(ii) x^3-1/x^3​

Answer 1

Answer:

Step-by-step explanation:

Given that,

2 ( x^2 + 1 ) = 5x ⇒ 2x^2 + 2 = 5x ⇒ 2x^2 + 2 - 5x = 0 ⇒ 2x ^2 - 5x + 2 = 0

⇒ 2x ^2 - 1x - 4x + 2 = 0 ⇒ x ( 2x - 1 ) - 2 ( 2x - 1 ) = 0

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

⇒ x = 2 or 2x = 1 ⇒ x = 2 or x = 1/2

∴ x = 2 or 1/2

(1) x - 1 / x

= 2 - 1 / 2 = 2 × 2 - 1 / 2 = 4 - 1 / 2 = 3 / 2 (∵we take x = 2 )

(2) x^3 - 1 / x ^3 = ( 2 )^3 - 1 / ( 2 ) ^3 = 8 - 1 / 8 = 8 × 8 - 1 / 8 = 64 - 1 / 8 = 63 / 8