已知:a+b=-8,ab=12,b*√(b/a)+a*√(a/b)

题目

已知:a+b=-8,ab=12,b*√(b/a)+a*√(a/b)
b*√(b/a)+a*√(a/b)
=b/a*√ab+a/b*√ab
=(b/a+a/b)√ab
=(a²+b²)/(√ab）这一步是怎麽来的
=[(a+b)²-2ab]/(√ab)
=(8²-24)/√12
=40/√12
=20√3/3

答案

b*√(b/a)+a*√(a/b)
=b/a*√ab+a/b*√ab
=(b/a+a/b)√ab
通分：b/a+a/b=b²/(ab)+a²/(ab)=(a²+b²)/(ab)
接下来：(a²+b²)/(ab)*√(ab)=(a²+b²)/(√ab）
=[(a+b)²-2ab]/(√ab)
=(8²-24)/√12
=40/√12
=20√3/3