SSC CPO SI and ASI 2013 Paper

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Question : 126 of 200

Marks: +1, -0

If

a^{2}+b^{2}=5 a b,

then the value of

( {a^{2}}/{b^{2}}+ {b^{2}}/{a^{2}} )

is

32
16
23
–23

Solution:

(3)

(a^{2}+b^{2} )^{2}=(5 a b)^{2}

⇒ a^{4}+b^{4}+2 a^{2} b^{2}=25 a^{2} b^{2}

⇒ a^{4}+b^{4}=23 a^{2} b^{2}

Hence

{a^{2}}/{b^{2}}+ {b^{2}}/{a^{2}}

= {a^{4}+b^{4}}/{a^{2} b^{2}}= {23 a^{2} b^{2}}/{a^{2} b^{2}}=23

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