Question

The sum of a number and its reciprocal is 1/3 the sum of their cubes is

Answer 1

-80/27 should be the ans of the que

Answer 2

The value of sum of the number and its cube is -26/27.

• The sum of the number and its reciprocal is 1/3.
• Let the number be x.
• Now the reciprocal will be 1/x.

x+1/x = 1/3

• Now cubing both sides we get,

x³ + 3x + 3/x +1/x³ = 1/27

• Now. we have to find the sum of cube of the number and the cube of its reciprocal.

x³ +1/x³ = 1/27 - 3x - 3/x

x³ +1/x³ = 1/27 - 3(x + 1/x)

x³ +1/x³ = 1/27 - 3(1/3)

x³ +1/x³ = -26/27

• Sum of number and it's cube is -26/27.