Question

x+1/x=3 then x^9+1/x9​

Answer 1

hey dear here is ur answer

x+1/x=3

x+1=3x

3x-x=1

2x=1

x=1/2

Answer 2

Answer:

Value of x^9+1/x9 is 5778.

Step-by-step explanation:

Given,

$x + \frac{1}{x} = 3$

Here we want to find

${x}^{9} + \frac{1}{ {x}^{9} } = {x}^{ {3}^{3} } + \frac{1}{ {x}^{ {3}^{3} } } \\ = ( {x}^{3} )^{3} +( \frac{1}{ {x}^{3} } )^{3} \\ = ( {x}^{3} + \frac{1}{ {x}^{3} } )^{3} - 3 {x}^{3} \times \frac{1}{ {x}^{3} } ( {x}^{3} + \frac{1}{ {x}^{3} } ) \\ = ( {x}^{3} + \frac{1}{ {x}^{3} } )^{3} - 3 ( {x}^{3} + \frac{1}{ {x}^{3} } ) .....(1)$

Now,

${x}^{3} + \frac{1}{ {x}^{3} } = (x + \frac{1}{x} )^{3} - 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) \\ = {(x + \frac{1}{x} )}^{3} - 3(x + \frac{1}{x} )$

We are putting value of $x + \frac{1}{x} = 3$

So,

${x}^{3} + \frac{1}{ {x}^{3} } = {3}^{3} - 3 \times 3 \\ = 27 - 9 \\ = 18$

Now from (1),

$( {x}^{3} + \frac{1}{ {x}^{3} } )^{3} - 3 ( {x}^{3} + \frac{1}{ {x}^{3} } ) \\ = {18}^{3} - 3 \times 18 \\ = 5832 - 54 \\ = 5778$

So,

${x}^{9} + \frac{1}{ {x}^{9} } = 5778$

Required value is

${a}^{3} + {b}^{3} = {(a + b)}^{3} - 3ab(a + b)$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549