x方加y方大于2xy

荆季柿1797已知x加y等于3,且xy等于负一,x方加y方等于多少 -
郟咱修15398258800 ______[答案] 因为x+y=3,所以(x+y)方等于9,xy等于-1,所以2xy等于-2.(X+y)方等于x方加y方再加上2xy.即x方加上y方-2=9,x方加Y方等于11.

荆季柿1797x平方加y平方小于等于1,求x方+2xy=y方的绝对值的最大值 -
郟咱修15398258800 ______[答案] |x^2+2xy+y^2|=|(x+y)^2|=(x+y)^2=x^2+y^2+2xy

荆季柿1797xy属于实数,求证x方加y方之和除以2大于等于x加y除以二的平方
郟咱修15398258800 ______ 要证(x²+y² )/2≥【(x+y)/2 】² 只要证 2(x²+y²)≥(x+y)² 也即x²+y² ≥2xy 显然成立 所以得证

荆季柿1797设x不等于y 证明2x平方加y平方大于2x加2xy减1 -
郟咱修15398258800 ______[答案] 设x不等于y 证明2x平方加y平方大于2x加2xy减1即,2x^2+y^2>2x+2xy-1证明:因为左-右=2x^2+y^2-2x-2xy+1=x^2-2xy+y^2+x^2-2x+1=(x-y)^2+(x-1)^2>=0由于x不等于y, 故(x-y)^2不等于0故(x-y)^2+(x-1)^2>0...

荆季柿1797若x方+Y方=1则xy/x+y+1的最大值为 -
郟咱修15398258800 ______[答案] (1).x²+y²=1.==>(x+y)²-1=2xy,===>(x+y+1)(x+y-1)=2xy.===>xy/(x+y+1)=(x+y-1)/2.故原式z=(x+y-1)/2.===>2z+1=x+y.(2).由均值不等式知,x²+y²≥2xy,===>2(x²+y²)≥x²+2xy+y²=(x+y)².===>√[2(x²+y²)]≥|x+y|≥x+y.又x²+y²=1,故x+y≤√2.===>2...

荆季柿1797x - y=2,x方+y方=10,求xy,(x+y)^2,x+y -
郟咱修15398258800 ______[答案] x-y=2 → (x-y)方=4 → x方+y方-2xy=4 → xy=(x方+y方-4)/2=(10-4)/2=3 (x+y)^2= x方+y方+2xy=10+2*3=16 x+y=(x+y)^2开方=±4

荆季柿1797实数x,y满足x方+y方=2x,则x方 - y方的最大值为________. -
郟咱修15398258800 ______[答案] 最大值是4 由x方+y方=2x得 x大于等于0 y方=2x-x方 得 (2x-x方)>=0 也就是0

荆季柿1797证明 x的4方加y的4方大于等于二分之一个xy(x+y)² -
郟咱修15398258800 ______[答案] 把右边的式子移到左边,并乘以2倍得到: x^4+y^4-0.5xy*(x+y)^2≥0证明这个不等式成立就可以了. 因为 2x^4+2y^4-xy*(x+y)^2 = 2x^4+2y^4-xy(x^2+2xy+y^2) = 2x^4+2y^4-x^3y-2(xy)^2-xy^3 = x^4+y^4-2(xy)^2+x^4+y^4-x^3y-xy^3 = (x^2-y^2)^2+x^3(x-y)-y^3(x...

荆季柿1797若x+y=8,x方*y方=4,求x方+y方. 急急急急急急急…… 答案:60或68. 求过程! -
郟咱修15398258800 ______[答案] x²y² = 4 因此: xy = 2 或者 xy = -2 x²+y² = x²+y² + 2xy - 2xy = (x+y)² - 2xy 当xy = 2时: x²+y² = x²+y² + 2xy - 2xy = (x+y)² - 2xy =64 - 4 =60 当xy = -2时: x²+y² = x²+y² + 2xy - 2xy = (x+y)² - 2xy =64 + 4 =68

荆季柿1797已知x的平方加上xy的和等于1,xy减去y的平方等于 - 4,则x的平方加上2xy减去y的平方等于?x方+xy=1,xy - y方= - 4,则x方+2xy - y方= -
郟咱修15398258800 ______[答案] x^2 +xy=1 xy-y^2=-4 所以两式相加即为:x^2 +xy+xy-y^2=x^2+2xy-y^2=-3