х² - 7х + 11 = 0,
Д = 49 - 44 = 5,
х1 = (7 + √5)/2,
х2 = (7 - √5)/2,
х1/х2 + х2/х1 =
= 1/2*(7 + √5) / 1/2*(7 - √5) + 1/2*(7 - √5) / 1/2(7 + √5) =
= (7 + √5)/(7 - √5) + (7 - √5)/(7 + √5) =
= (7 + √5)(7 + √5)/(7 - √5)(7 + √5) + (7 - √5)(7 - √5)/(7 - √5)(7 + √5) =
= ((7 + √5)² + (7 - √5)²) / (7² - (√5)²) =
= (49 + 14√5 + 5 + 49 - 14√5 + 5) / (49 - 5) =
= 108/44 = 2 20/44 = 2 5/11
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Answers & Comments
х² - 7х + 11 = 0,
Д = 49 - 44 = 5,
х1 = (7 + √5)/2,
х2 = (7 - √5)/2,
х1/х2 + х2/х1 =
= 1/2*(7 + √5) / 1/2*(7 - √5) + 1/2*(7 - √5) / 1/2(7 + √5) =
= (7 + √5)/(7 - √5) + (7 - √5)/(7 + √5) =
= (7 + √5)(7 + √5)/(7 - √5)(7 + √5) + (7 - √5)(7 - √5)/(7 - √5)(7 + √5) =
= ((7 + √5)² + (7 - √5)²) / (7² - (√5)²) =
= (49 + 14√5 + 5 + 49 - 14√5 + 5) / (49 - 5) =
= 108/44 = 2 20/44 = 2 5/11