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已知x>1,y>0,且2/(x%1)+1/y =2,求x+y最小值

其实题目是关系到“1”的妙用。 对于1/x+9/y=2,两边除以2,则 (1/2)·(1/x+9/y)=1, 所以, x+y=1·(x+y) =(1/2)(1/x+9/y)·(x+y) =(1/2)(10+y/x+9x/y) ≥(1/2)[10+2√(y/x·9x/y)] =(1/2)(10+6) =8, 即1/x+9/y=2且y/x=9x/y, x=2,y=6时, 所求x+y最...

解: 2/(x-1)+1/y=2 2/(x-1)=2- 1/y x>1,x-1>0,2/(x-1)>0 2-1/y>0,1/y0,因此y>½ (首先判定y的取值范围) 整理,得x=(4y-1)/(2y-1) (再将x用y表示) x+y=(4y-1)/(2y-1) +y =(4y-2+1)/(2y-1) +y =y+2 +1/(2y-1) =½(2y-1) +1/(2y-1) +5...

x>0,y>0, ∴1=2/x+1/y =(√2)^2/x+1^2/y ≥(√2+1)^2/(x+y) ∴x+y≥3+2√2. 故所求最小值为;3+2√2。

y=(1/x+1/y)(x+2y)=1+2+2y/x+x/y=3+(2y/x+x/y) ≥ 3+2√(2y/x)*(x/y)=3+2√2 当且仅当,2y/x=x/y,x=√2y时,等号成立 最小值=3+2√2 y=1/x+1/y的最小值=3+2√2

1/x2+1/y2+1/xy≥3 * 3^√ ̄1/x2*y2*xy =3 * 3^√ ̄1/x^3*y^3 x+y=2≥2√ ̄xy 所以√ ̄xy ≤1 所以 3 * 3^√ ̄1/x^3*y^3≤3

x>0 y>0 则x+y>0 xy>0 1/x+1/y=2 (x+y)/(xy)=2 x+y=2xy 由均值不等式得4xy≤(x+y)²,xy≤(x+y)²/4 因此x+y≤2(x+y)²/4 整理,得 (x+y)²-2(x+y)≥0 (x+y)(x+y-2)≥0 x+y≥2或x+y≤0(舍去) x+y的最小值是2,此时x=y=1。

x>y>0,x+y≤2, ∴2/(x+3y)+1/(x-y) =(√2)²/(x+3y)+1²/(x-y) ≥(√2+1)²/[(x+3y)+(x-y)] =(3+2√2)/[2(x+y)] ≥(3+2√2)/4. 故(x+3y):√2=(x-y):1且x+y=2, 即x=-1+2√2,y=3-2√2时, 所求最小值为: (3+2√2)/4。

解: 2/x +1/y=1 1/y=1- 2/x=(x-2)/x y=x/(x-2) x>0,y>0,x/(x-2)>0,x>2 x+2y=x+ 2x/(x-2) =x+2(x-2+2)/(x-2) =x +2 +4/(x-2) =(x-2)+ 4/(x-2) +4 x>2,x-2>0,由均值不等式得: (x-2)+ 4/(x-2)≥2√[(x-2)·4/(x-2)]=4 (x-2)+ 4/(x-2) +4≥8 x+2y...

x>y>0且x+y≤2, 故依均值不等式得 2/(x+3y)+1/(x-y) =1·[2/(x+3y)+1/(x-y)] =[(x+3y)+(x-y)]/4·[2/(x+3y)+1/(x-y)] =3/4+(1/4)·[(x+3y)/(x-y)+2(x-y)/(x+3y)] ≥3/4+(1/4)·2√[(x+3y)/(x-y)·2(x-y)/(x+3y)] =(3+2√2)/4. ∴(x+3y)/(x-y)=2(x-y)/(x+3...

(8/x)+(2/y)=((8/x)+(2/y))(x+y)=(8+2+8y/x+2x/y) 大于等于(10+2*根号下((8y/x)*(2x/y)))=18 (8/x)+(2/y)的最小值=18

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