Question

1.已知x>0,y>0,3x+4y=5,求xy的最大值.2.求函数y=x*2+7x+10/x+1(x＞-1)的最小值

Answer 1

1.已知x>0,y>0,3x+4y=5,求xy的最大值.

5=3x+4y≥2√3x·4y

5/2≥√12xy

25/4≥12xy

xy≤25/48

即最大值=25/48

2.求函数y=x*2+7x+10/x+1(x＞-1)的最小值 急!

y=x*2+7x+10/x+1

=[(x+1)平方+5x+5+1]/(x+1)

=(x+1) +5 +1/(x+1)

=(x+1) +1/(x+1)+5

≥2√(x+1)·1/(x+1) +5

=2+5

=7

最小值=7