1, let l: x/a+y/b = 1, where a >；; 0, b>0, if the straight line passes through point m (2, 1), then 2/a+ 1/b = 1, using the basic inequality, there is1= 2/a+1/b ≥ 2.
2. Average annual growth rate (P+Q)/2. Suppose last year was a, then this year is A (1+P), next year is A (1+P) (1+Q), and if the average annual growth rate is x, then last year is A (1+X), and next year is a (/kloc-0). That is, a (1+p) (1+q) = a (1+x)? x =√[( 1+p)( 1+q)]- 1。 This problem is to compare the sizes of (p+q)/2 and √ [(1+p) (1+q)]-1 Consider √ [(1+p)]-1≤ [(1+p)+(1+q)]/2-1= (.
3. If both X and Y are within (0, 1), then both log values are positive, then S≤[(㏒? X+㏒？ Y)/2]？ = = (radix is 1/3, right? ) == 1, considering that the condition of obtaining equal sign is not met (equal sign is taken when equal), so this question chooses B;
4.A (-2,-1) is replaced by point coordinates, with 2m+n = 1. 1/m+2/n = (2m+n) (1/m+2/n) = 4+n/m+4m/n ≥ 8, if and only if n/m=4m/n is n? =4m？ Take the equal sign (satisfying the condition of using basic inequality), and the minimum value is 8.
Note: when using basic inequalities, we must pay attention to the conditions: positive, definite and so on.