If x^2+3 x+1=0, then what is the value of x^6+\frac{1}{x^6} ?

SSC CGL 3 Mar 2020 Shift 2 Paper

Question : 53 of 75

Marks: +1, -0

x^2+3 x+1=0

, then what is the value of

x^6+\;{1}/{x^6} ?

Solution:

x^2+3 x+1=0

Dividing the equation by

{\x}

x+1 \/ x=-3

We know that
If

x+1 \/ x=a

then

(x)^2+1 \/(x)^2=(a)^2-2

and

(x)^3+1 \/(x)^3=(a)^3-3 a

Now,

( {\x})^3+1 \/( {\x})^3=(-3)^3-3 ×(-3)

⇒( {\x})^3+1 \/( {\x})^3=-27+9=-18

{\x}^6+1 \/ {\x}^6=(-18)^2-2

⇒ {\x}^6+1 \/ {\x}^6=324-2=322

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