已知x,y∈R,满足(x²+y²+2)(x²+y²-1)-18≤0.求证:xy≤
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/07 03:11:02
已知x,y∈R,满足(x²+y²+2)(x²+y²-1)-18≤0.求证:xy≤2
![已知x,y∈R,满足(x²+y²+2)(x²+y²-1)-18≤0.求证:xy≤](/uploads/image/z/18626337-9-7.jpg?t=%E5%B7%B2%E7%9F%A5x%2Cy%E2%88%88R%2C%E6%BB%A1%E8%B6%B3%EF%BC%88x%26sup2%3B%2By%26sup2%3B%2B2%29%28x%26sup2%3B%2By%26sup2%3B-1%29-18%E2%89%A40.%E6%B1%82%E8%AF%81%EF%BC%9Axy%E2%89%A4)
(x²+y²+2)(x²+y²-1)≤18等价于(x²+y²)^2+(x²+y²)≤20
2xy*(2xy+1)≤(x²+y²)^2+(x²+y²)≤20
(2xy+1/2)^2-1/4≤20
(2xy+1/2)^2≤81/4
2xy+1/2≤9/2
2xy≤4
xy≤2
2xy*(2xy+1)≤(x²+y²)^2+(x²+y²)≤20
(2xy+1/2)^2-1/4≤20
(2xy+1/2)^2≤81/4
2xy+1/2≤9/2
2xy≤4
xy≤2
1-x²+2xy-y²
计算:(1).(-2xy²)*(3x²y)²
已知xy=8满足x²y-xy²-x+y=56,求x²+y²
已知x²y²+x²+y²=10xy-16 求x,y
已知实数x,y满足x²+4y²=4.求f(x,y)=x²+2xy+4y²+x+2
已知x/y=3,求x²+2xy-3y²/x²-2xy+y²
已知x/y=3,求x²+2xy-3y²/x²-xy+y²的值
x²-4y²/x²+2xy+y²÷x+2y/2x²+2xy
1、已知xy满足(x+1)²+1y+21=0试求-2xy·5x²y+(0.5x²y&sup
已知3x²+xy-2y²=0.求代数式y分之x-x分之y-xy分之x²+y²的值
已知m=x²+y²/x²+y²,n=2xy/x²+y²,则下
已知X²-5XY+6Y²=0,求(X²+3XY)\2Y²的值