質問: 設x+y=4 xy=1 求y/x+1+x/y+1? 設x+y=4 xy=1 求y/x+1+x/y+1?
回答: y x ------ + ------- x+1 y+1 y(y+1) + x( x+1) = ---------------------- (x+1)(y+1) y2+y + x2+x = ---------------- xy+x+y+1 x2+y2 + (x +y) = ---------------- ---- xy + (x+y) +1 x2+y2 + 4 = ------------- 1 + 4 +1 (x2+2xy+y2)-2xy + 4 = --------------------------- 6 (x+y)2-2xy + 4 = -------------------- 6 42-2(1)+ 4 = --------------- 6 = 3