Question

if x+1/x=3 then find value of x3+1/x3

Answer 1

$\textbf{Answer}$

We need to find,
$\textbf{ x^3 + 1/x^3 }$

We are given,
$\textbf{ x + 1/x = 3 }$


We know that,
$\textbf{ (a+b)^3 = a^3 + b^3 + 3ab(a+b) }$

Lets take the cube of both sides of the given equation,
=> (x + 1/x)^3 = 3^3

=> x^3 + 1/x^3 + {3 . x . 1/x (x + 1/x)} = 27

=> x^3 + 1/x^3 + 3(x + 1/x) = 27

Since x + 1/x = 3

=> x^3 + 1/x^3 + 3×3 = 27

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

=> $\textbf{x^3 + 1/x^3 = 18}$



$\textbf{Hope It Helps}$

$\textbf{Thanks}$

Answer 2

Answer is 36

Step-by-step explanation:

x - 1 / x = 3

( x - 1 / x ) = ( 3 )³

Using Identity :

( a - b )³ = a³ - b³ - 3 ab ( a - b )

⇒ x³ - 1 / x³ - 3 ( x - 1 / x ) = 27

⇒ x³ - 1 / x³ - 3 ( 3 ) = 27

⇒ x³ - 1 / x³ - 9 = 27

⇒ x³ - 1 / x³ = 27 + 9

⇒ x³ - 1 / x³ = 36

Therefore; your answer iz 36

Hope it helps!

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