Question

求下列各组数的比例中项(1)7+根号5与7-根号5(2)a^4+a^2b^2与b^4+a^2b^2

Answer 1

1)

(7+根号5)(7-根号5 )

=49-5

=44,

比例中项为±2√11,

2)(a^4+a^2b^2)(b^4+a^2b^2)

=a^2b^2(a^2+b^2)(b^2+a^2)

=a^2b^2(a^2+b^2)^2

比例中项为：±ab(a^2+b^2)