已知正实数x,y满足x+y+1/x+9/y=10,则x+y的最大值是
问题描述:
已知正实数x,y满足x+y+1/x+9/y=10,则x+y的最大值是
答
因为 x+y+1/x+9/y=10所以 (x+y)(x+y+1/x+9/y)=10(x+y)(x+y)²+(x+y)/x +9(x+y)/y=10(x+y)(x+y)²+y/x+9x/y +10=10(x+y) (1)因为 y/x +9x/y≥2√[(y/x)(9x/y)]=6,(当且仅当 y=3x 时 取等号)所以 (1)式...