是否還有個(gè)條件:a+b=10?
x+y= (x+y)•1
=( x+y)( a/x+b/y)
=a+ bx/y+ ay/x+b
= bx/y+ ay/x+ a +b
≥2√(bx/y• ay/x) + a +b
=2√(ab) + a +b
=(√a+√b)²,
當(dāng)且僅當(dāng)bx/y= ay/x時(shí)取到等號(hào).
x+y的最小值為18,所以(√a+√b)²=18,
又因a+b=10,
所以a=2,b=8或a=8,b=2.