Question

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


please tell me the answer​

Answer 1

Given :

• x + 1/x = 3

To find :

• value of x³+1/x³

Solution :

x + 1/x = 3

(x - 1/x)³ = 3³

x³ + 1/x³ + 3x 1/x (x + 1/x) = 27

x³ + 1/x³ + 3 × 3 = 27

x³ + 1/x³ + 9 = 27

x³ + 1/x³ = 27 - 9

x³ + 1/x³ = 18

∴ Value of x³+1/x³ is 18

Answer 2

Answer:

Given :-

▪️x + $\dfrac{1}{x}$ = 3

To Find :-

▪️ x³ + $\dfrac{1}{x³}$ = ?

Solution :-

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

By cubing both sides we get,

=> ( x + $\dfrac{1}{x}$ )³ = (3)³

=> x³ + 3.x².$\dfrac{1}{x}$ + 3.x.$\dfrac{1}{x²}$ + $\dfrac{1}{x³}$ = 27

=> ( x³ + $\dfrac{1}{x³}$ ) + 3.x².$\dfrac{1}{x}$ + 3.x.$\dfrac{1}{x²}$ = 27

=> x³ + $\dfrac{1}{x³}$ + ( 3x + $\dfrac{3}{x}$ ) = 27

=> x³ + $\dfrac{1}{x³}$ + 3(x + $\dfrac{1}{x}$) = 27

=> x³ + $\dfrac{1}{x³}$ + 3 × 3 = 27

=> x³ + $\dfrac{1}{x³}$ + 9 = 27

=> x³ + $\dfrac{1}{x³}$ = 27 - 9

$\dashrightarrow$ x³ + $\dfrac{1}{x³}$ = 18

Hence, the value of x³ + $\dfrac{1}{x³}$ = 18

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