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已知x+y=2.xy=½.求1.½x²+½y&#...

1题 1/2[(x+y)^2-2xy]=3/2 2题 xy[(x+y)^2]=2

解: x=2代入曲线方程,得 2²-2y+y²=7 y²-2y-3=0 (y+1)(y-3)=0 y=-1或y=3 x²-xy+y²=7,等式两边同时求导 2x-(y+xy')+2yy'=7 y'=(2x-y-7)/(x-2y) x=2,y=-1时,y'=[2·2-(-1)-7]/[2-2·(-1)]=-½ y-(-1)=-½(x-2)...

x²+y²-xy+2x-y+1 =[3(x+1)²+(x-2y+1)²]/4 =0, 由于(x+1)²>=0且(x-2y+1)²>=0, 则有x+1=x-2y+1=0,解得x=-1,y=0,

x²+xy+1/4y²+3/4y²-3y+3=0 (x+1/2y)²+3/4(y-2)²=0 ∴x+1/2y=0 y-2=0 ∴x=-1 y=2 ∴x^y=(-1)²=1

x²-xy+y²=1 (x-½y)²+(√3y/2)²=1 令x-½y=cosθ,√3y/2=sinθ 则x=cosθ+sinθ/√3,y=2sinθ/√3 x²+2y² =(cosθ+sinθ/√3)²+2(2sinθ/√3)² =cos²θ+2sinθcosθ/√3+3sin²θ =2+sin2θ/√3 -cos2θ =...

解: 1. x+y=2 (x+1)+(y+1)=2+2=4 xy=1 (x+1)(y+1)=xy+(x+y)+2=1+2+2=5 (y+1)/(x+1)+ (x+1)/(y+1) =[(x+1)²+(y+1)²]/[(x+1)(y+1)] =[(x+1+y+1)²-2(x+1)(y+1)]/[(x+1)(y+1)] =(4²-2×5)/5 =6/5 2. 分式有意义,a-b≠0,b-c≠0,...

已知x+y=2;xy=-1/2 那么x²+y²=(x+y)²-2xy=2²-2*(-1/2)=5 所以(x-y)²=x²+y²-2xy=5-2*(-1/2)=6 如果不懂,请追问,祝学习愉快!

解: (x-2)(x+2)+y²=0 x²-4+y²=0 x²+y²=4 令x=2cosα,y=2sinα 3xy=3·2cosα·2sinα=6·2sinαcosα=6sin(2α) -1≤sin(2α)≤1 -6≤6sin(2α)≤6 -6≤3xy≤6 3xy的最大值为6,最小值为-6

(1) 1/2=1²/(x+1)+1²/(y+1) ≥(1+1)²/[(ⅹ+1)+(y+1)] ⇔x+y+2≥8 ⇔x+y≥6. 故x=y=3时, 所求x+y最小值为6. (2) 1/(x+1)+1/(y+1)=1/2 ⇔xy=x+y+3≥2√(xy)+3. 设√(xy)=t,代入上式得 t²≥2t+3 解得,t≥(1+√13)/2. ∴...

(x+y)^2=1,(x-y)^2=49两式相加得:2(x²+y²)=50x²+y²=25两式相减得:4xy=-48xy=-12

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