Question

If x-1/x = p then show that:(x^3-1/x^3)= p^3 + 3p

Answer 1

Answer:

Step-by-step explanation:

In the question it is given that,

x - 1/x = p

Now, cubing on both sides, we get,

( x - 1/x ) ^3 = p^3      expanding,

x3 - 1/x3  - 3( x - 1/x) = p3

x3 - 1/x3 = p3 + 3( x - 1/x)                  --- x - 1/x = p

therefore, x3 - 1/x3 = p3 + 3p

Hence, proved.

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Answer 2

Note :

★ (a + b)² = a² + 2ab + b²

★ (a - b)² = a² - 2ab + b²

★ (a + b)(a - b) = a² - b²

★ (a + b)² = (a - b)² + 4ab

★ (a + b)³ = a³ + b³ + 3ab(a + b)

★ (a - b)³ = a³ - b³ - 3ab(a - b)

Solution :

• Given : x - 1/x = p
• To prove : x³ - 1/x³ = p³ + 3p

Proof :

We have ;

x - 1/x = p

Now ,

Cubing both the sides , we get ;

=> (x - 1/x)³ = p³

=> x³ - (1/x)³ - 3•x•(1/x)•(x - 1/x) = p³

=> x³ - 1/x³ - 3(x - 1/x) = p³

=> x³ - 1/x³ - 3p = p³

=> x³ - 1/x³ = p³ + 3p

Hence proved .