Question

设集合A=（y|y=-4x2+6）,B=（x|y=根号x-3）,则A交B=

Answer 1

A=（y|y=-4x^2+6）,B={x|y=√(x-3）},

B={x|y=√(x-3）},

={x|x= y^2 + 3}

={y|y= x^2 + 3}

for A∩B

-4x^2+6 = x^2 + 3

5x^2=3

x =3√5/5 or - 3√5/5

from A : y=-4x^2+6

for x= 3√5/5 => y=18/5

for x= -3√5/5 => y=18/5

A∩B = { 18/5 } #