Question
If x = √7 + √6 and y = √7 - √6 ,
then the value of is (x2 + y2)/(x3 + y3).Solution
x = √7 + √6 and y = √7 - √6 x + y = √7 + √6 + √7 - √6 = 2√7 xy = √7 + √6 x √7 - √6 xy = 1 x2 + y2 = (x + y)2 - 2xy x3 + y3 = (x + y)3 - 3xy(x + y) (x2 + y2)/(x3 + y3) = ((x + y)2 - 2xy)/((x + y)3 - 3xy(x + y)) = ((2√7)2 - 2 x 1)/((2√7)3 - 3 x 1(2√7)) = (4 x 7 - 2)/(8 x 7 x √7 - 6√7) (28-2)/(56√7 - 6√7) = 26/(50 √7) = 13/(25√7) 13/(25√7) x √7/√7 = (13√7)/(25 x 7) = (13√7)/175
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