Question

answer it and then step by step explain it... fully describe it plz!!! I need this. no spamming!!​

Answer 1

Answer:

2√5

Step-by-Step Explanation:

Note : x2=x², x3=x³

(x^6+1)/x³=x^6/x³ + 1/x³

x2+1/x2=3

=>x2 + 1/x2 + 2=3+2

Using property (a+1/a)2=a2 + 1/a2 + 2 :

=>(x+1/x)^2=5

=>x+1/x=√5

Cubing both sides:

=>(x+1/x)^3=(√5)^3

Using identity (a+1/a)3=a3 + 1/a3 + 3(a+1/a):

=>x3+1/x3 + 3(x+1/x)=5√5

Substituting x+1/x with √5:

=>x3+1/x3 + 3√5=5√5

=>x3+1/x3=2√5

Substituting back:

=>((x^6)+1)/x3=2√5