Question

If x= root 3 + root 2 ÷ root 3 - root 2 and y = root 3 - root 2 ÷ root 3+ root 2 find the value of x²+y²​

Answer 1

Answer:

x = ( √3 + √2 ) / ( √3 - √2 )

  = ( √3 + √2 ) ( √3 + √2 ) / ( √3 + √2 )( √3 - √2 )

  = ( √3 + √2 )² / ( 3 - 2 )

  = 3 + 2 √6 + 2

  = 5 + 2√6

x² = ( 5 + 2√6 )²

   = 25 + 20√6 + 24

   = 49 + 20√6

y = ( √3 - √2 ) /( √3 + √2 )

  = ( √3 - √2 )( √3 - √2 ) / ( √3 - √2 )( √3 + √2 )

  = ( √3 - √2 )² / ( 3 - 2  )

  = 3 - 2 √6 + 2

  = 5 - 2√6

y² = ( 5 - 2√6 )²

   = 25 - 20 √6 + 24

   = 49 - 20 √6

x² + y² = 49 + 20√6 +49 - 20 √6

          = 98 ( answer )

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