If x^{4}-6 x^{2}-1=0, then the value of x^{6}-5 x^{2}+ {5}/{x^{2}}-{1}/{x^{6}}+5 is:

SSC CGL 7 06 2019 Shift 2 Paper

Question : 52 of 100

Marks: +1, -0

x^{4}-6 x^{2}-1=0,

then the value of

x^{6}-5 x^{2}+\ {5}/{x^{2}}-

\ {1}/{x^{6}}+5

is:

Solution:

\ { x}^{4}-6 \ {x}^{2}-1=0

\ {x}^{4}-1=6 \ {x}^{2}

\⇒\ {x}^{2}-\ {1}/{\ {x}^{2}}=6

\ {\Now}, \ {x}^{6}-\ {1}/{\ {x}^{6}}

=6^{3}+3(6)

=234

\ {\ATQ}

\ {x}^{6}-5 \ {x}^{2}+\ {5}/{\ {x}^{2}}-\ {1}/{\ {x}^{6}}+5

\⇒\ {x}^{6}-\ {1}/{\ {x}^{6}}-5\ [\ {x}^{2}-\ {1}/{\ {x}^{2}}\ ]+5

\⇒234-5(6)+5

\⇒209

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