若有理数a,b满足ab不等于0,且（a^2+b^2)^3=(a^3+b^3)^2+8a^3b^3,求a/b+b/a的值请写出过程._数学解答

若有理数a,b满足ab不等于0,且（a^2+b^2)^3=(a^3+b^3)^2+8a^3b^3,求a/b+b/a的值
请写出过程.

人气：258 ℃　时间：2020-05-19 07:22:16

解答

（a^2+b^2)^3=(a^3+b^3)^2+8a^3b^3a^6+3a^4b^2+3a^2b^4+b^6=a^6+b^62a^3b^3+8a^3b^33a^4b^2+3a^2b^4=10a^3b^33a^2+3b^2=10ab3a^2/10ab+3b^2/10ab=13/10(a/b+b/a)=1a/b+b/a=10/3