<span><span><span><span>14<span>x2</span></span>−<span>5x</span></span>−1</span>=0</span>
<span>Коэффициенты уравнения: </span>
<span>a=14</span><span>, </span><span>b=<span>−5</span></span><span>, </span><span>c=<span>−1</span></span>
<span>Вычислим дискриминант: </span>
<span><span>D=<span><span>b2</span>−<span><span>4a</span>c</span></span></span>=</span><span><span><span><span><span>(<span>−5</span>)</span>2</span>−<span><span>4·14</span>·<span>(<span>−1</span>)</span></span></span>=<span>25+56</span></span>=81</span>
<span>(<span>D>0</span>)</span>, следовательно это квадратное уравнение имеет 2 различных вещественных корня:
Вычислим корни:
<span><span>x<span>(<span>1,2</span>)</span></span>=<span><span><span>−b</span>±<span>√D</span></span><span>2a</span></span></span><span><span><span><span><span><span>x1</span>=<span><span><span>−b</span>+<span>√D</span></span><span>2a</span></span></span>=<span><span><span>−<span>(<span>−5</span>)</span></span>+9</span><span>2·14</span></span></span>=<span>1428</span></span>=0</span>,5</span><span><span><span><span><span><span>x2</span>=<span><span><span>−b</span>−<span>√D</span></span><span>2a</span></span></span>=<span><span><span>−<span>(<span>−5</span>)</span></span>−9</span><span>2·14</span></span></span>=<span><span>−4</span>28</span></span>=<span>−0</span></span>,143</span>
<span><span><span><span><span>14<span>x2</span></span>−<span>5x</span></span>−1</span>=<span><span>(<span><span>x−0</span>,5</span>)</span><span>(<span><span>x+0</span>,143</span>)</span></span></span>=0</span>Ответ:
<span><span><span>x1</span>=0</span>,5</span>
<span><span><span>x2</span>=<span>−0</span></span>,<span>143
</span></span>
2^(x-1)+2^(x+3>17 2^x*2^(-1)+2^x*2^3>17 2^x(1/2+8)>17 2^x(17/2)>17 2^x/2>1
2^(x-1)>1 2^(x-1>2^0 x-1>0 x>1
значение этой функции при х=-4 равно y=-3x=-3*(-4)=12
Неравенство верно всегда, когда выполняется ОДЗ и х не равен 0.Ответ: х больше 0.
