x 2 + x 2 1 = x 2 + 2 ⋅ x ⋅ x 1 + ( x 1 ) 2 − 2 ⋅ x ⋅ x 1 = ( x + x 1 ) 2 − 2 x = 2 + 3 ⇒ x + x 1 = 2 + 3 + 2 + 3 1 = 2 + 3 + ( 2 + 3 ) ( 2 − 3 ) 2 − 3 = = 2 + 3 + 4 − 3 2 − 3 = 2 + 3 + 2 − 3 = 4 x + x 1 = 4 ⇒ ( x + x 1 ) 2 − 2 = 4 2 − 2 = 16 − 2 = 14
x²+1/x² = ( x + 1/ x ) 2 - 2 * x * ( 1 / x) = ( 2 + √3 + 2 - √3)^2 - 2 = 16 - 2 = 14.
The value of x 2 + x 2 1 when x = 2 + 3 is 14 . We determined this by calculating x + x 1 and applying the identity x 2 + x 2 1 = ( x + x 1 ) 2 − 2 .
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