Given (x + y) ^ 2 = m, (X-Y) ^ 2 = n, try to use Mn to express (1) XY (2) x / y + Y / X
(x+y)^2=m (1)
(x-y)^2=n (2)
From (1)
x²+2xy+y²=m (3)
From (2)
x²-2xy+y²=n (4)
(3) - (4) get
4xy=m-n
∴xy=(m-n)/4
(3) + (4) get
2x²+2y²=m+n
∴x²+y²=(m+n)/2
x/y+y/x=(x²+y²)/xy=[(m+n)/2]/[(m-n)/4]=2(m+n)/(m-n)
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