Question

X + 1 by X equals to 3 then find the value of x cube + 1 by x cube​

Answer 1

x + 1/x = 3

Cubing both the sides,

(x + 1/x)³ = (3)³

Now using the identity

(a + b)³ = a³ + b³ + 3ab(a + b)

=> (x + 1/x)³ = (3)³

=> x³ + 1/x³ + 3x × 1/x(x + 1/x) = 27

=> x³ + 1/x³ + 3(x + 1/x) = 27

=> x³ + 1/x³ + 3(3) = 27

(since x + 1/x = 3 given)

=> x³ + 1/x³ + 9 = 27

=> x³ + 1/x³ = 27 - 9

=> x³ + 1/x³ = 18

Hope this helps!