设集合M={(x,y)|x2+y2=1,x∈R,y∈R},N={(x,y)|x2-y=0,x∈R,y∈R},则集合M∩N是多少_数学解答

设集合M={(x,y)|x2+y2=1,x∈R,y∈R},N={(x,y)|x2-y=0,x∈R,y∈R},则集合M∩N是多少

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解答

联立 x²+y²=1x² - y = 0 即 x² = y ≥ 0消x ：y²+y -1 = 0y = (-1+√5)/2 或 y = (-1-√5)/2 （小于0,舍去）x² = (-1+√5)/2x = ± √[ (-1+√5)/2]M∩N = { （√[ (-1+√5)/2] ,(-1+...