If x^{4}+x^{-4}=194, x>0, then the value of (x-2)^{2} is

SSC CGL 4 06 2019 Shift 1 Paper

Question : 75 of 100

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x^{4}+x^{-4}=194, x>0,

then the value of

(x-2)^{2}

Solution:

x^{4}+\ {1}/{x^{4}}=194

x^{4}+\ {1}/{x^{4}}+2=196

(x^{2}+\ {1}/{x^{2}}\ )^{2}=196

x^{2}+\ {1}/{x^{2}}=14

x^{2}+\ {1}/{x^{2}}+2=16

x+\ {1}/{x}=4

x^{2}+1=4 x

\⇒x^{2}-4 x+1=0

x^{2}-4 x+4=3

(x-2)^{2}=3

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