Question

x-ix=5 then find out x^3+1/x^3

Answer 1

Question :

If x - 1/x = 5 then find x³ + 1/x³ .

Answer :

x³ + 1/x³ = 26√29

Solution :

• Given : x - 1/x = 5
• To find : x³ + 1/x³

We know that ;

(a + b)² = (a - b)² + 4ab

Thus ,

=> (x + 1/x)² = (x - 1/x)² + 4•x•(1/x)

=> (x + 1/x)² = 5² + 4

=> (x + 1/x)² = 25 + 4

=> (x + 1/x)² = 29

=> x + 1/x = √29

Also ,

We know that ,

(a + b)³ = a³ + b³ + 3ab(a + b)

Thus ,

=> (x + 1/x)³ = x³ + (1/x)³ + 3•x•(1/x)•(x + 1/x)

=> (√29)³ = x³ + 1/x³ + 3√29

=> 29√29 = x³ + 1/x³ + 3√29

=> x³ + 1/x³ = 29√29 - 3√29

=> x³ + 1/x³ = 26√29

Hence , x³ + 1/x³ = 26√29 .