Question

已知a+b=-8,ab=8,将b根号b/a+a根号a/b化简并求值

Answer 1

由题知（b根号b/a+a根号a/b）值小于零
因为（b根号b/a+a根号a/b）^2
=b^3/a+a^3/b+2ab
=(a^4+b^4+2a^2b^2)/(ab)
=(a^2+b^2)^2/(ab)
=((a+b)^2-2ab)^2/(ab)
=((-8)^2-2*8)^2/8
=48^2/8
所以：b根号b/a+a根号a/b
=-48/(根号8）
=-12根号2

Answer 2

∵a+b=-8<0，ab=8>0
∴a<0 b<0
∴b√(b/a)+a√(a/b)
=b√(ab/a²)+a√(ab/b²)
=-(b/a)√(ab)-(a/b)√(ab)
=[-(a²+b²)/ab]√(ab)
=-[(a+b)²-2ab]/ab*√(ab)
=-(64-16)/8*2√2
=-12√2