Question

X+1/X=6 then what is the value of x6+1/x6=?​

Answer 1

Answer:

Step-by-step explanation:

x−1x=6(1)

(x−1x)2=(6)2

x2+1x2=36+2=38(2)

(x+1x)2=x2+1x2+2=38+2=40

x+1x=40−−√=±210−−√(3)

(x−1x)3=(6)3

x3−1x3−3(x−1x)=216

x3−1x3=216+3×6=234(4)

(x+1x)3=(±210−−√)3

x3+1x3+3(x+1x)=±8010−−√

x3+1x3=±8010−−√∓3×210−−√=±7410−−√(5)

(4)×(5)⟹

(x3−1x3)(x3+1x3)=234×(±7410−−√)

(x6−1x6)=±1731610−−√

x6−1x6=±1731610−−√  

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