SSC CGL 10 Aug 2017 Shift 1 Paper

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Question : 62 of 100

Marks: +1, -0

If

x + 1/x=3,

then what is the value of

{x^4 + 5x^3 + 3x ^2+5x +1}/{x^4+1}

?.

$25/7$
4
$31/7$
$33/7$

Solution:

x + 1/x=3

On squaring both sides,

x^2 + 1/x^2+2=9

⇒

x^2 + 1/x^2=7

∴

x^4 +1 = 7 x^2

{x ^4 + 5x^3 + 3x^2 + 5x + 1}/{x^4 + 1}

={x ^4 + 5x^3 + 3x^2 + 5x + 1}/{7x^2 }

=1/7[x^2+5x+3+5/x+1/x^2]

=1/7[x^2+1/x^2+5(x+1/x)+3]

=1/7[7 + 5× 3 +3]

=1/7[7+15+3]=25/7

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