Question

if x2-6x-1=0 find x3-1/x3

Answer 1

Answer :

x³ - 1/x³ = 234

Solution :

• Given : x² - 6x - 1 = 0
• To find : x³ - 1/x³ = 0

We have ,

=> x² - 6x - 1 = 0

=> x² - 1 = 6x

=> (x² - 1)/x = 6

=> x²/x - 1/x = 6

=> x - 1/x = 6

Now ,

Cubing both the sides , we get ;

=> (x - 1/x)³ = 6³

=> x³ - (1/x)³ - 3•x•(1/x)•(x - 1/x) = 216

=> x³ - 1/x³ - 3•1•6 = 216

=> x³ - 1/x³ - 18 = 216

=> x³ - 1/x³ = 216 + 18

=> x³ - 1/x³ = 234

Hence ,

x³ - 1/x³ = 234