Question

plese see the picture and solve the question​

Answer 1

||✪✪ QUESTION ✪✪||

if (x - 1/x) = 1/3 find the value of (x)³ - 1/(x)³ ?

|| ✰✰ ANSWER ✰✰ ||

(x -1/x) = 1/3

Cubing both sides and using (a-b)³ = a³ - b³ - 3ab(a-b) in LHS , we get,

→ x³ - 1/x³ - 3 * x * 1/x ( x - 1/x) = (1/3)³

→ x³ - 1/x³ - 3 * (x - 1/x) = 1/27

Putting value of (x - 1/x) = 1/3 in LHS now,

→ x³ - 1/x³ - 3 * 1/3 = 1/27

→ x³ - 1/x³ - 1 = 1/27

→ x³ - 1/x³ = (1/27) + 1

→ x³ - 1/x³ = (1 + 27)/27

→ x³ - 1/x³ = (28/27) (Ans).

Answer 2

Given :-

• (x - 1/x) = 3

To Find :-

• x³ - 1/x³ = ?

Formula used :-

• (a-b)³ = a³ - b³ - 3ab(a-b)

Solution :-

(x -1/x) = 1/3

Cubing both sides

=> x³ - 1/x³ - 3 * x * 1/x ( x - 1/x) = (1/3)³

=> x³ - 1/x³ - 3 * (x - 1/x) = 1/27

Putting value of (x - 1/x) = 1/3 in LHS now,

=> x³ - 1/x³ - 3 * 1/3 = 1/27

=> x³ - 1/x³ - 1 = 1/27

=> x³ - 1/x³ = (1/27) + 1

=> x³ - 1/x³ = (1 + 27)/27

=> x³ - 1/x³ = (28/27)

So, x³ - 1/x³ is Equal to 28/27.