If a + 1/a = p, prove that a3 + 1/a3 = p (p2 – 3).

If a + 1/a = p, prove that a³ + 1/a³ = p (p² – 3).

Answer :

We know that

a³ + 1/a³ = (a + 1/a)³ – 3a (1/a) (a + 1/a)

Substituting the values

a³ + 1/a³ = p³ – 3p

Taking p as common

a³ + 1/a³ = p (p² – 3)

Therefore, it is proved.

More Solutions:

• If (x + 1/x)2 = 3, find x3 + 1/x3.
• If x = 5 – 2√6, find the value of √x + 1/√x.
• If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2.
• If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.
• If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.
• If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.
• Find the value of ab – bc – ca.
• If a – b = 7 and a2 + b2 = 85, then find the value of a3 – b3.
• Find the product of x and y.
• Find the sum of their cubes.