Math plz help x,y是兩個不相等的實數,且[√(x²+1)+x] [√(y²+1)+y] =1,求x+y的值.?

令 x+y = k
y = k-x , 代回原式得:
[ √(x²+1) + x ] [ √( k²-2kx+x²+1) + k-x ] = 1
√(k²-2kx+x²+1) + k-x = 1 / [ √(x²+1) + x ] = √(x²+1) - x
√(k²-2kx+x²+1) = √(x²+1) - k
等式兩邊平方, 等式恆成立:
k²-2kx+x²+1 = x²+1+k² - 2k√(x²+1)
-2kx = - 2k√(x²+1)
2k * [ √(x²+1) - x ] = 0
因為 √(x²+1) > x , 所以 √(x²+1) - x ≠ 0
故 k = 0

Ans: 0