x+3y+5xy+求3x+4y的最小值

车孟盼3390若正数x,y满足x+3y=5xy,则3x+4y的最小值是 -
逄炉炭15692395943 ______ 因为x+3y=5xy 两边同除以5xy 1/5y+3/5x=13x+4y=(3x+4y)(1/5y+3/5x)=9/5+4/5+3x/5y+12y/5x≥13/5+2倍根号36/25=5

车孟盼3390x>0 y>0且x+3y=5xy求3x+4y的min -
逄炉炭15692395943 ______ ∵x+3y=5xy,且x,y>0∴两边同除以xy,可得(1/y)+(3/x)=5∴由柯西不等式可得:5(3x+4y)=[(3/x)+(1/y)]*(3x+4y)≥(3+2)²=25∴3x+4y≥5∴(3x+4y)min=5

车孟盼3390x+3y=5xy 则3x+4y的最小值是? -
逄炉炭15692395943 ______ 【【注:可能缺少一个条件,就是x, y>0】】 解: ∵x+3y=5xy,且x,y>0 ∴两边同除以xy,可得 (1/y)+(3/x)=5 ∴由柯西不等式可得: 5(3x+4y) =[(3/x)+(1/y)]*(3x+4y)≥(3+2)²=25 ∴3x+4y≥5 ∴(3x+4y)min=5

车孟盼3390x+3y=5xy,(x,y>0)求3x+y最小值 -
逄炉炭15692395943 ______ x+3y=5xy x(5y-1) =3y x = 3y/(5y-1) S = 3x +y =9y/(5y-1) +y = (9/5)+ (9/5)[1/(5y-1)] +y S' = -(9)[1/(5y-1)^2] +1 =0 (5y-1)^2-9=0 25y^2-10y-8=0 (5y+2)(5y-4)=0 y= 4/5 S'' = (90)[1/(5y-1)^3] S''(4/5)>0 (min) S = 9y/(5y-1) +y minS = S(4/5) S(4/5) = (36/5)/3 + 4/5 = 12/5 +4/5 =16/5

车孟盼3390若正数xy满足x加三y等于五xy则三x加四y的最小值是 -
逄炉炭15692395943 ______ x+3y=5xy 3x+4y=(3x+4y)*(x+3y)/5xy=(3x^2+13xy+12Y^2)/5xy=1/5*(13+3x/y+12y/x)≥1/5*(13+2√3x/y*12y/x)=1/5*(13+12)=5

车孟盼3390若正数x,y满足x+3y=5xy,则3x+4y的最小值是( ) -
逄炉炭15692395943 ______[选项] A. 24 5 B. 28 5 C. 5 D. 6

车孟盼3390若正数x,y满足x+3y=5xy,则3x+4y的最小值是( )A.245B.285C.6D.5 -
逄炉炭15692395943 ______[答案] ∵正数x,y满足x+3y=5xy, ∴ x+3y 5xy=1,即 1 5y+ 3 5x=1, ∴3x+4y=(3x+4y)( 1 5y+ 3 5x) = 13 5+ 3x 5y+ 12y 5x≥ 13 5+2 3x5y•12y5x=5 当且仅当 3x 5y= 12y 5x即x=1且y= 1 2时取等号, ∴3x+4y的最小值为:5 故选:D

车孟盼3390已知x+y=5xy,求(3x+xy+3y)/(x - 2xy+y)
逄炉炭15692395943 ______ (3x+xy+3y)/(x-2xy+y) =[3(x+y)+xy]/(x+y-2xy) =(3*5xy+xy)/(5xy-2xy) =(16xy)/(3xy) =16/3

车孟盼3390正数x,y满足x+3y=5xy,则3x+4y最小值是5 -
逄炉炭15692395943 ______ 用x+3y≥2√3xy ,代入得5xy≥2√3xy ,求出xy最小值(12/25) 这一部取得等号的条件是 x=3y 然后用3x+4y≥2√12xy 代入xy最小值12/25 这一步取得等号的条件是3x=4y 两部的极值都是在等号时候取得的,而两步取得极值的条件又是不同的,故不能取得此时的极值.

车孟盼3390 若正数x,y满足x+3y=5xy,则3x+4y的最小值是( ) A. B. C.5 D.6 -
逄炉炭15692395943 ______[答案] C ∵正数x,y满足x+3y=5xy, ∴=1 ∴3x+4y=()(3x+4y)=+++≥+2=5 当且仅当=时取等号 ∴3x+4y≥5 即3x+4y的最小值是5 故选C