若实数x,y满足x的平方+2√3x+根号(x+y+1)+3=0,求代数式(1/x-y+1/x+y)÷y/(x²
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若实数x,y满足x的平方+2√3x+根号(x+y+1)+3=0,求代数式(1/x-y+1/x+y)÷y/(x²+y²)
重点是代入部分啊
重点是代入部分啊
![若实数x,y满足x的平方+2√3x+根号(x+y+1)+3=0,求代数式(1/x-y+1/x+y)÷y/(x²](/uploads/image/z/2066244-60-4.jpg?t=%E8%8B%A5%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3x%E7%9A%84%E5%B9%B3%E6%96%B9%2B2%E2%88%9A3x%2B%E6%A0%B9%E5%8F%B7%EF%BC%88x%2By%2B1%EF%BC%89%2B3%3D0%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F%281%2Fx-y%2B1%2Fx%2By%29%C3%B7y%2F%EF%BC%88x%26%23178%3B)
若实数x,y满足x²+2√3x+√(x+y+1)+3=0,求代数式[1/(x-y)+1/(x+y)]÷y/(x²+y²)的值
x²+2√3x+√(x+y+1)+3=(x+√3)²+√(x+y+1)=0
故x=-√3,y=-x-1=√3-1;于是:
x²+y²=3+(√3-1)²=3+(3-2√3+1)=7-2√3;
x²-y²=3-(√3-1)²=3-(3-2√3+1)=2√3-1
[1/(x-y)+1/(x+y)]÷y/(x²+y²)=[2x/(x²-y²)]×[(x²+y²)/y]=[2x(x²+y²)]/[y(x²-y²)]
=[-2(√3)(7-2√3)]/[(√3-1)(2√3-1)]=(-14√3+12)/(6-2√3-√3+1)=(-14√3+12)/(7-3√3)
=(-14√3+12)(7+3√3)/22=(-7√3+6)(7+3√3)/11=(-49√3+42-63+18√3)/11=-(21+31√3)/11
再问: 不是应该把代数式化简吗
再答: 已经化简到不能再化的程度了。
x²+2√3x+√(x+y+1)+3=(x+√3)²+√(x+y+1)=0
故x=-√3,y=-x-1=√3-1;于是:
x²+y²=3+(√3-1)²=3+(3-2√3+1)=7-2√3;
x²-y²=3-(√3-1)²=3-(3-2√3+1)=2√3-1
[1/(x-y)+1/(x+y)]÷y/(x²+y²)=[2x/(x²-y²)]×[(x²+y²)/y]=[2x(x²+y²)]/[y(x²-y²)]
=[-2(√3)(7-2√3)]/[(√3-1)(2√3-1)]=(-14√3+12)/(6-2√3-√3+1)=(-14√3+12)/(7-3√3)
=(-14√3+12)(7+3√3)/22=(-7√3+6)(7+3√3)/11=(-49√3+42-63+18√3)/11=-(21+31√3)/11
再问: 不是应该把代数式化简吗
再答: 已经化简到不能再化的程度了。
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