If  and  then the value of  = ?

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SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 2)
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Answer (Detailed Solution Below)

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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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Given:

  and 

Calculations:

According to question,

  

⇒x = 9 - 4√5

⇒x² = 161 - 72√5

and  

⇒y = 9 + 4√5

⇒y² = 161 + 72√5

Now, 

 

= (161 - 72√5 - 1 + 161 + 72√5)/(161 - 72√5 + 1 + 161 + 72√5)

= (322 - 1)/(322 + 1)

= 321/323

Hence, The Required value is 321/323.

Alternate Method

We know, if x =  and y =  then (x + y) = 

  and   so, x + y =  = 18 and xy = 1

So,  =  =  = 321/323

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