a,b属于正实数,a+b=1,求(1+1/a)(1+1/b)>=9 .
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a>0，b>0，所以有
a+b≥2√(ab)
1≥2√(ab)
ab≤1/4
1/(ab)≥4
(1+1/a)(1+1/b)
=1+1/a+1/b+1/(ab)
=1+(1/a+1/b)+1/(ab)
=1+(a+b)/(ab)+1/(ab)
=1+1/(ab)+1/(ab)
=1+2/(ab)
≥1+2×4
=9
即(1+1/a)(1+1/b)≥9
a+b≥2√(ab)
1≥2√(ab)
ab≤1/4
1/(ab)≥4
(1+1/a)(1+1/b)
=1+1/a+1/b+1/(ab)
=1+(1/a+1/b)+1/(ab)
=1+(a+b)/(ab)+1/(ab)
=1+1/(ab)+1/(ab)
=1+2/(ab)
≥1+2×4
=9
即(1+1/a)(1+1/b)≥9
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