正整数x,y满足x2-y2=2xy,求x-y/x+y的值
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正整数x,y满足x2-y2=2xy,求x-y/x+y的值
正整数x,y满足x2-y2=2xy,求x-y/x+y的值
正整数x,y满足x2-y2=2xy,求x-y/x+y的值
(X+Y)²=X²+Y²+2XY=X²+Y²+X²-Y²=2X²
(X-Y)²=X²+Y²-2XY=X²+Y²-X²+Y²=2Y²
(X-Y)²/(X+Y)²=Y²/X²
X-Y/X+Y=Y/X
X²-Y²=2XY
1-(Y/X)²=2Y/X
Y/X=-1±√2
X-Y/X+Y=-1±√2
X²-Y²=2XY,求X-Y/X+Y
(X+Y)²=X²+Y²+2XY=X²+Y²+X²-Y²=2X²
(X-Y)²=X²+Y²-2XY=X²+Y²-X²+Y²=2Y²
(X-Y)...
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X²-Y²=2XY,求X-Y/X+Y
(X+Y)²=X²+Y²+2XY=X²+Y²+X²-Y²=2X²
(X-Y)²=X²+Y²-2XY=X²+Y²-X²+Y²=2Y²
(X-Y)²/(X+Y)²=Y²/X²
X-Y/X+Y=Y/X
X²-Y²=2XY
1-(Y/X)²=2Y/X
Y/X=-1±√2
X-Y/X+Y=-1±√2
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因为x2-y2=2xy,且x,y均为正整数,
所以,两边同时除以xy, x/y -y/x =2
令x/y =A
则有 A -1/A =2
解之得:A=1 +根号2,即 x/y =1 +根号2 ,即x =(1 +根号2)y
所以, (x-y)/(x+y) =根号2 - 1
x2-y2=2xy