第2章方程式と不等式Equations and Inequalities

Key Equations重要な式

quadratic formula二次方程式の解の公式	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Distance距離	$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$
Slope of a line直線の傾き	$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Point-Slope equation of a line直線の点傾き形の方程式	$y - y_{1} = m (x - x_{1})$
Adding Complex Numbers複素数の加法	$(a + b i) + (c + d i) = (a + c) + (b + d) i$
Subtracting Complex Numbers複素数の減法	$(a + b i) - (c + d i) = (a - c) + (b - d) i$
Square Root Property平方根の性質	$If x^{2} = k then x = \pm \sqrt{k}$
Quadratic Formula二次方程式の解の公式	$If a x^{2} + b x + c = 0 then x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
Rational Exponents有理数の指数	$a^{\frac{m}{n}} = {(a^{\frac{1}{n}})}^{m} = {(a^{m})}^{\frac{1}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}$
Absolute Value絶対値	$If x \geq 0, \| x \| = x; If x < 0, \| x \| = - x$
Addition Property of Inequalities不等式の加法の性質	$If a < b then a + c < b + c$
Multiplication Property of Inequalities不等式の乗法の性質	$\begin{matrix} If a < b and c > 0, then a c < b c \\ If a < b and c < 0, then a c > b c \end{matrix}$