Question

a,b为实数,且a+b=-8,ab=8,求b∫b/a+a∫a/b的值

Answer 1

原式=b/a∫ab+a/b∫ab
=b²/ab∫ab+a²/ab∫ab
=a²+b²/ab∫ab
=[(a+b)²－2ab]/ab∫ab
∵a+b=－8 ab=8
∴原式=[(－8)²-2×8]/8∫8
=48/8×2∫2
=6×2∫2
=12∫2

追答

Answer 2

b√b/a +a√a/b
=1/√ab *( -b^2 -a^2)
那么a^2+b^2=(a+b)^2 -2ab=48
所以代入得到
b√b/a +a√a/b
= 1/√8 *(-48)= -12√2

Answer 3

原式=b/a∫ab+a/b∫ab
=b²/ab∫ab+a²/ab∫ab
=a²+b²/ab∫ab
=[(a+b)²－2ab]/ab∫ab
∵a+b=－8 ab=8
∴原式=[(－8)²-2×8]/8∫8
=48/8×2∫2
=6×2∫2
=12∫2