如集合M=｛X|y=x^2+1,x属于R｝,N={x|=3-y^2}则M交N=?要解答详细过程谢谢急!

Question

如集合M=｛X|y=x^2+1,x属于R｝,N={x|=3-y^2}则M交N=?要解答详细过程 谢谢 急!

Answer 1

N={x| x=3-y^2 }
M={x| y=x^2+1,x∈R｝
={x| x= √(y-1) or -√(y-1),x∈R｝
M∩N =>
3-y^2 = (+/-)√(y-1) ( y>1)
(3-y^2)^2 = y-1
y^4-6y^2-y+10 =0
(y-2)(y^3+2y^2-2y -5)=0
y = 2
x= 3-4 = -1
M∩N = { -1}