If (a+ \frac{1}{a} )=-2 then the value of a^{1000}+a^{-1000}is

SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 75 of 100

Marks: +1, -0

(a+ {1}/{a} )=-2

then the value of

a^{1000}+a^{-1000}

Solution:

(1)

a+ {1}/{a}=-2

⇒ a^{2}+1=-2 a

⇒ a^{2}+2 a+1=0

⇒(a+1)^{2}=0

⇒ a+1=0

⇒ a=-1

∴(a)^{1000}+(a)^{-1000}

=(-1)^{1000}+(-1)^{-1000}

=1+1=2

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