Question

If x-1/x=5, find the value of x^3-1/x^3

Answer 1

65 is the answer. Solve the first equation and then plug in.

Answer 2

Here,

x-1/x=5,

To find out

x³-1/x³

We know that,

Cubing on both side

( x -1/x)³ = (5)³

→ x³ - 1/x³ - 3× x × 1/x ( x - 1/x ) = 125

→ x³ - 1/x³ - 3 × 5 = 125

→ x³ - 1/x³ - 15 = 125

→ x³ - 1/x³ = 125 + 15

→ x³ - 1/x³ = 140

Thus,

• x³-1/x³ = 140

_______________________________________________________________________

More Information

`\sf \: (x + y) {}^(2) = {x}^(2) + {y}^(2) + 2xy`

`\sf \: (x - y) {}^(2) = {x}^(2) + {y}^(2) - 2xy`

`\sf \: \: (x + y)(x + - y) = x {}^(2) - {y}^(2)`

`\sf \: ({x} - y {} ) {}^(3) = x {}^(3) - y {}^(3) - 3a {}^(2) b \: + 3ab {}^(2) \\ \\ \sf \: ({x} + y {} ) {}^(3) = x {}^(3) + y {}^(3) + 3a {}^(2) b \: + 3ab {}^(2)`