Question

If x-1/x=√5 find x^3+1/x^3x

Answer 1

Step-by-step explanation:

x-1/x=√5

(x-1/x)²=5

(x+1/x)²-4=5

(x+1/x)²=9

x+1/x=3.........(1)

(x+1/x)²=9

x²+1/x²+2=9

x²+1/x²=7

now,

x³+1/x³=(x+1/x)(x²+1/x²-1)

x³+1/x³=(3)(7-1)

x³+1/x³=18