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已知x=根号2-1⼀根号2+1,y=根号2+1⼀根号2-1,求x-y⼀x2+y2

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2024年12月04日 15:08

有2个网友回答

网友（1）：

x=√2+1,y=√2-1,则x-y=2,xy=1,
(x-y)�0�5=x�0�5+y�0�5-2xy=4则 x�0�5+y�0�5=6所以（x+y)�0�5= x�0�5+y�0�5+2xy=8所以x+y=2√2则 x-y/2x+2y=2/2（x+y)=2/4√2=√2/4

网友（2）：

x = (√2 -1) / (√2 + 1) = (√2 -1)^2 = 3 -2√2y = (√2 +1) / (√2 - 1) = (√2 +1)^2 = 3 +2√2 x - y = (3- 2√2) -(3 + 2√2) = - 4√2x^2 + y^2 = (3 -2√2)^2 + (3 + 2√2)^2 = 2 * (9 + 8) = 34 (x-y) / (x^2 +y^2) = (-4√2( / 34 = -(2√2 )/ 17