Question

求a^4+a^2b^2与b^4+a^2b^2的等比中项

速度``详细点~~
谢谢了`

Answer 1

(a^4+a^2b^2)(b^4+a^2b^2)
=a^2(a^2+b^2)*b^2(b^2+a^2)
=a^2b^2(a^2+b^2)^2
所以,等比中项=√((a^4+a^2b^2)(b^4+a^2b^2))
=√(a^2b^2(a^2+b^2)^2)
=±ab(a^2+b^2)

Answer 2

(a^4+a^2b^2)*(b^4+a^2b^2)
=a^4b^4+a^2b^6+a^4b^4+a^6b^2
=a^2b^2(a^2b^2+b^4+a^2b^2+a^4)
=a^2b^2(a^2+b^2)^2

所以等比中项为ab(a^2+b^2)或-ab(a^2+b^2)

Answer 3

±√[(a^4+a^2b^2)(b^4+a^2b^2)]
=±（a^3b+ab^3）

Answer 4

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

所以等比中项为ab(a^2+b^2)或－ab(a^2+b^2)

Answer 5

等比中项公式：G*2=a×b 我算得a×b×根号下(a*2+b*2)