共50条信息
已知正实数\(x\),\(y\)满足\(x+y+3=xy\),若对任意满足条件的\(x\),\(y\),都有\({{(x+y)}^{2}}-a(x+y)+1\geqslant 0\)恒成立,则实数\({a}\)的取值范围为________
已知\(a > b\),二次不等式\(ax^{2}+2x+b\geqslant 0\)对于一切实数\(x\)恒成立,又存在\(x_{0}∈R\),\(ax_{0}^{2}+2x_{0}+b=0\),则\(\dfrac{a^{2}{+}b^{2}}{a\mathrm{{-}}b}\)的最小值为____\(.\)
已知\(b > a > 0,\)且\(a+b=1\),那么( )
已知正数\(x\),\(y\)满足\(\dfrac{1}{x}+\dfrac{1}{y}=1\),那么\(\dfrac{4x}{x\mathrm{{-}}1}+\dfrac{9y}{y\mathrm{{-}}1}\)的最小值为 \(.\)
设\(a\),\(b∈R+\),且\(a+b=4\),则有( )
设函数\(f\left( x \right)={{x}^{2}}+aIn\left( 1+x \right)\)有两个极值点\(x_{1}\),\(x_{2}\),且\({{x}_{1}} < {{x}_{2}}\)
\((I)\)求\(a\)的取值范围,并讨论\(f\left( x \right)\)的单调性;
\((II)\)证明:\(f\left( {{x}_{2}} \right) > \dfrac{1-2In2}{4}\)
已知函数\(f(x)=\log _{a}x+m(a > 0\)且\(a\neq 1)\)的图象过点\((8,2)\),点\(P(3,-1)\)关于直线\(x=2\)的对称点\(Q\)在\(f(x)\)的图象上.
\((1)\)求函数\(f(x)\)的解析式;
\((2)\)令\(g(x)=2f(x)-f(x-1)\),求\(g(x)\)的最小值及取得最小值时\(x\)的值.
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