以知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围已知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围`
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![以知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围已知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围`](/uploads/image/z/6932976-24-6.jpg?t=%E4%BB%A5%E7%9F%A5%E5%AE%9E%E6%95%B0%E5%AF%B9%EF%BC%88a%2Cb%EF%BC%89%E6%BB%A1%E8%B6%B3a%5E2%2Bab%2Bb%5E2%3D1%60%E4%BB%A4k%3Da%5E2-ab%2Bb%5E2%60%E6%B1%82K%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0%E5%AF%B9%EF%BC%88a%2Cb%EF%BC%89%E6%BB%A1%E8%B6%B3a%5E2%2Bab%2Bb%5E2%3D1%60%E4%BB%A4k%3Da%5E2-ab%2Bb%5E2%60%E6%B1%82K%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%60)
以知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围已知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围`
以知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围
已知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围`
以知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围已知实数对(a,b)满足a^2+ab+b^2=1`令k=a^2-ab+b^2`求K的取值范围`
a^2+ab+b^2=1
(a+b)^2=1+ab
得出1+ab》=0故ab》=-1
由
a^2+b^2-2ab=1-3ab
得出(a-b)^2》=0故ab《=1 /3
得出-1《=ab《=1/3
k=a^2-ab+b^2`
故k=(a+b)^2-3ab
k=1+ab-3ab
k=1-2ab
故得出3》=k》=-1/3.
a^2+ab+b^2=1
(a+b)^2=1+ab
得出1+ab》=0故ab》=-1
由
a^2+b^2=1-ab
得出1-ab》=0故ab《=1
得出-1《=ab《=1
k=a^2-ab+b^2`
故k=(a+b)^2-3ab
k=1+ab-3ab
k=1-2ab
故得出3》=k》=-1.
答案应该是 1/3 <= k <= 3 理由如下:
从 -1 <= ab <= 1/3 开始
由上一步得 -2 <= 2ab <= 2/3
故 2=> -2ab => -2/3
则 2+1 => -2ab+1 => -2/3+1
即 3 =>1-2ab => 1/3
所以 3 => k => 1/3
故 1/3 <= k <= 3