Question

x+1/x root of 29 then what is the x3+1/x3

Answer 1

Given : x + 1/x  = √29

To Find : x³ - 1/x³

Solution:

x + 1/x  = √29

Squaring both sides

=> x²  + 1/x²  + 2x(1/x) = 29

=> x²  + 1/x²  +  2 = 29

=>  x²  + 1/x²  = 27

=>  x²  + 1/x² - 2 = 25

=> x²  + 1/x² - 2x(1/x) = 25

=> (x - 1/x)²  = 5²

=> x  - 1/x  = 5

cubing both sides

=> x³  - 1/x³  - 3x(1/x)(x - 1/x)  = 5³

=>x³ - 1/x³  - 3(5) = 125

=> x³ - 1/x³ = 140

x³ - 1/x³ = 140