(√12 -√75) · √ 12 = √ 12 · √ 12 - √ 75 · √12 = (√12)² - √(12 · 75) = 12 - √900 = 12 - 30 = -18
Формулы: loga b/loga c= logc b ----> log2 6 / log2 9=log9 6
loga b=1/logb a ----->log9 6 = 1/log6 9
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log2 6 * log6 9 / log2 9 = (log2 6 / log2 9)*log6 9=
=log9 6 * log6 9=log6 9 / log6 9 =1
ответ 1
1) Нули функции :
![3x^2+7x-4=0\\D=\sqrt{7^2-4*3*(-4)} =\sqrt{97}\\\\x_1=\frac{-7+\sqrt{97}}{6} \\\\x_2=\frac{-7-\sqrt{97}}{6}](https://tex.z-dn.net/?f=3x%5E2%2B7x-4%3D0%5C%5CD%3D%5Csqrt%7B7%5E2-4%2A3%2A%28-4%29%7D%20%3D%5Csqrt%7B97%7D%5C%5C%5C%5Cx_1%3D%5Cfrac%7B-7%2B%5Csqrt%7B97%7D%7D%7B6%7D%20%5C%5C%5C%5Cx_2%3D%5Cfrac%7B-7-%5Csqrt%7B97%7D%7D%7B6%7D)
Получились странные корни, можно найти приближенное значение
x1 ≈ 0.47
x2 ≈ -2.8
2) Доп. точки для построения
С Оу : (0; -4)
3) Вершина:
![x_0=-\frac{b}{2a} =-\frac{7}{6} =-1\frac{1}{6} \\\\y_0=3(-\frac{7}{6})^2+7(-\frac{7}{6})-4=3*\frac{49}{36} -\frac{49}{6} -4=\frac{49}{12} -\frac{49}{6} -4=\frac{49-98-48}{12} =-\frac{97}{12}=-8\frac{1}{12}](https://tex.z-dn.net/?f=x_0%3D-%5Cfrac%7Bb%7D%7B2a%7D%20%3D-%5Cfrac%7B7%7D%7B6%7D%20%3D-1%5Cfrac%7B1%7D%7B6%7D%20%5C%5C%5C%5Cy_0%3D3%28-%5Cfrac%7B7%7D%7B6%7D%29%5E2%2B7%28-%5Cfrac%7B7%7D%7B6%7D%29-4%3D3%2A%5Cfrac%7B49%7D%7B36%7D%20-%5Cfrac%7B49%7D%7B6%7D%20-4%3D%5Cfrac%7B49%7D%7B12%7D%20-%5Cfrac%7B49%7D%7B6%7D%20-4%3D%5Cfrac%7B49-98-48%7D%7B12%7D%20%3D-%5Cfrac%7B97%7D%7B12%7D%3D-8%5Cfrac%7B1%7D%7B12%7D)
![(-1\frac{1}{6} ; -8\frac{1}{12} )](https://tex.z-dn.net/?f=%28-1%5Cfrac%7B1%7D%7B6%7D%20%3B%20-8%5Cfrac%7B1%7D%7B12%7D%20%29)