y=(5x²+9x+4)/(x²+1)的值域
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y=(5x²+9x+4)/(x²+1)的值域
y=(5x²+9x+4)/(x²+1)的值域
y=(5x²+9x+4)/(x²+1)的值域
分母写成平方差形式,分子则凑成5(x方-1)+9(x+1),化简之后,就变成了,5+9/(x-1) 则y不等于5 y属于R
y=(5x^2+9x+4)/(x^2+1),
——》5x^2+9x+4=y(x^2+1),
——》(5-y)x^2+9x+(4-y)=0,
方程有解,则:
判别式△=81-4(5-y)(4-y)>=0,
——》y^2-9y-1/4<=0,
——》(9-√82)/2<=y<=(9+√82)/2。