Question

if x+1/x = 9, then find the value of x^3 + 1/x^3 by a^3 + b^3 identity ​

Answer 1

Answer:

x³ + 1/x³ = 702

Note:

★ (a + b)² = a² + 2ab + b²

★ (a - b)² = a² - 2ab + b²

★ a² - b² = (a + b)(a - b)

★ (a + b)³ = a³ + b³ + 3ab(a + b)

★ (a - b)³ = a³ + b³ - 3ab(a - b)

★ a³ + b³ = (a + b)(a² - ab + b²)

★ a³ - b³ = (a - b)(a² + ab + b²)

Solution:

Given: x + 1/x = 9

To find: x³ + 1/x³ = ?

Now,

x³ + 1/x³ = (x + 1/x)•[x² - x•(1/x) + (1/x)²]

= (x + 1/x)•[x² - 1 + 1/x²]

= (x + 1/x)•[ x² + 2 + 1/x² - 3 ]

= (x + 1/x)•[ x² + 2•x•(1/x) + 1/x² - 3 ]

= (x + 1/x)•[ (x + 1/x)² - 3 ]

= 9•[ 9² - 3 ]

= 9•[81 - 3]

= 9•78

= 702

Hence,

Required answer is 702 .