Question

设a大于b大于0,a^2+b^2-6ab=0，则(a+b)/(a-b)的值等于多少

写出详细的过程 谢谢了
写错了- -、
设a大于b大于0,a^2+b^2-6ab=0，则(a+b)/(b-a)的值等于多少

Answer 1

a^2+b^2=6ab
等号两边都加2ab就得到a^2+b^2+2ab=8ab
即（a+b）^2=8ab;
等号两边都减2ab就得到a^2+b^2-2ab=4ab
即(a-b)^2=4ab
所以（a+b）^2/(a-b)^2=8ab/4ab=2
两边开方就得到结果a+b/a-b=正负根号2

Answer 2

a^2+b^2-6ab=0
则
a^2+b^2+2ab=8ab=(a+b)^2
a^2+b^2-2ab=4ab=(a-b)^2
(a+b)^2/(a-b)^2=8ab/(4ab)=4
(a+b)/(a-b)=2

Answer 3

a^2+b^2-6ab=0
(a+b)^2=8ab,a+b=2√(2ab)
(a-b)^2=4ab,a-b=2√(ab)
(a+b)/(b-a)=-√2

Answer 4

2

Answer 5

(a+b)^2=8ab
(a-b)^2=4ab
(a+b)^2/(a-b)^2=4
(a+b)/(a-b)=2