Question

if x+1/x=3 what is x^3+1/x^3=​

Answer 1

Answer:

Required value of x^3 + 1 / x^3 is 18

Step-by-step explanation:

Here,

x + 1 / x = 3

Cubing on both sides :

= > ( x + 1 / x )^3 = 3^3

= > x^3 + ( 1 / x )^3 + 3( x × 1 / x )( x + 1 / x ) = 27 { Using ( a + b )^3 = a^3 + b^3 + 3ab( a + b ) }

= > x^3 + 1 / x^3 + 3( 1 )( 3 ) = 27 { x + 1 / x = 3, from question }

= > x^3 + 1 / x^3 + 9 = 27

= > x^3 + 1 / x^3 = 18

Hence the required value of x^3 + 1 / x^3 is 18.

Answer 2

Question :-

$\texttt{if} \: x \: + \frac{1}{x} = 3 \: \texttt{then\: find \:} {x}^{3} + \frac{1}{ {x}^{3} }$

Answer :-

$\implies \: \red{\boxed{ {x}^{3} + \frac{1}{ {x}^{3} } = 18} \: }$

Formula used:-

$\star \boxed{ {(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)}$

Step - by - step explanation :-

Given that,

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

Taking cube on both sides,

$\rightarrow \: { \bigg(x + \frac{1}{x} \bigg)}^{3} = {(3)}^{3}$

Using the given formula,

$\small {x}^{3} + { \big( \frac{1}{x} \big)}^{3} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 27 \\ \\ \rightarrow \: {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times (3) = 27 \\ \because \: x + \frac{1}{x} = 3 \\ \\ \rightarrow \: \boxed{ {x}^{3} + \frac{1}{ {x}^{3} } = 18}$