If x+1/x=\sqrt3 then the value of x^6 + 1is

SSC CPO SI and ASI Model Paper 7

Question : 144 of 200

Marks: +1, -0

x+1/x=√3

then the value of

x^6 + 1

Solution:

(3)

x+1/x=√3

⇒

[x+1/x]^2=(√3)^2

⇒x^2+1/x^2+22=3

⇒x^2+1/x^2=1

multiplying both side by

[x+1/x]

we get

[x+1/x][x^2+1/x^2]=[x+1/x]

⇒x^3+1/x+x+1/x^3=x+1/x

⇒x^3+1/x^3=0⇒x^6+1/x^3=0

⇒x^6+1=0

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