Question

square + 1 upon x square is equal to 83 find the value of x cube minus one upon x cube​

Answer 1

Answer:

756

Step-by-step explanation:

(a - b)² = a² + b² - 2ab

a² + b² = 2ab + (a - b)²

In the problem let's assume x = a and 1/x = b then,

x² + 1/x² = 83

(2 × x × 1/x) + (x - 1/x)² = 83

2 + (x - 1/x)² = 83

(x - 1/x)² = 83 - 2

(x - 1/x)² = 81

x - 1/x = √81

x - 1/x = 9

(a - b)³ = a³ - b³ - 3ab(a - b)

a³ - b³ = (a - b)³ + 3ab(a - b)

x³ - 1/x³ = (x - 1/x)³ + (3 × x × 1/x(x - 1/x))

= 9³ + (3 × 9)

= 756