Question

If x=7+4√3 and xy = 1 , what is the value of 1/x2+1/y2 ?

Answer 1

Hi ,

x = 7 + 4√3 ---( 1 )

xy = 1 ( given )

y = 1/x = 1/ ( 7 + 4√3 )

= ( 7 - 4√3 ) / [ (7+4√3)(7-4√3)]

= ( 7 - 4√3 ) /[ 7² - ( 4√3 )² ]

= ( 7 - 4√3) / ( 49 - 48 )

= 7 - 4√3 ----( 2 )

Now ,

1/x² + 1/y²

= ( y² + x² ) / x² y²

= ( x² + y² ) / ( xy )²

= [(7+4√3)²+(7-4√3)²]/[(7+4√3)(7-4√3)]²

= 2[ 7² + ( 4√3)² ]/1

= 2[ 49 + 48 ]

= 2 × 97

= 194

I hope this helps you.

: )

Answer 2

Answer:

194 is your answer

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