Question

if x²- 2x =1 ,find the value of x³-1/x³​

Answer 1

Answer:

x³ - 1/x³ = 364.

Step-by-step explanation:

Given : x² + 1/x² = 51

We know that, (x - 1/x)² = x² + (1/x)² - 2 × x × 1/x  

[By using identity , (a - b)²  = a² + b² - 2ab]

(x - 1/x)² = x² + 1/x² - 2  

(x - 1/x)² = 51 - 2

(x - 1/x)² = 49

(x - 1/x) = ± √7

[Taking square root on both sides]

x - 1/x = ± 7

On cubing both sides,  

(x - 1/x)³ = (7)³

x³ - 1/x³ - 3 x × 1/x (x - 1/x) = 343

x³ - 1/x³ - 3 (x - 1/x) = 343

x³ - 1/x³ - 3 (7) = 343

x³ - 1/x³ - 21 = 343

x³ - 1/x³  = 343 + 21

x³ - 1/x³ = 364

Hence the value of x³ - 1/x³ is 364.