Question

if x=2+√3, find the value of x³+1/x³​

Answer 1

Answer:

18

Step-by-step explanation:

SOLUTION

X² + 1/x² = 7

(x + 1/x)² -2.x.1/x = 7

(x + 1/x )² -2 = 7  

(x + 1/x )² = 9

take square root both sides  

(x + 1/x) = 3  

then,  

x³ + 1/x³ = ( x + 1/x)³ - 3.x.1/x(x + 1/x)  

= ( x +1/x)³ -3(x + 1/x)

= (3)³ -3(3)  

= 27 - 9

= 18