More about equations：練習問題

Solve the equation $$6(x + 1) = -2x + 14$$.

Solve the equation \( 3^{2x+2} - 10 \cdot 3^x + 1 = 0 \).

Solve the fractional equation:
$$\frac{2x}{x-1} - \frac{1}{x+1} = \frac{4}{x^2-1}$$

Solve the equation \(2 \cos^2 \theta + \cos \theta - 1 = 0\) for \(0^\circ \le \theta \le 180^\circ\).

Solve the equation \( 2^{2x+2} - 5 \cdot 2^x + 1 = 0 \).

Solve the equation \(25^x - 6 \cdot 5^x + 5 = 0\).

Solve the fractional equation $$\frac{1}{x-3} + \frac{2}{x+4} = 2$$.

Solve the fractional equation $$\frac{4}{x+3} + \frac{1}{x-2} = 1$$.

The sum of a non-zero real number \( x \) and twice its reciprocal is \( 3.3 \).

(a) Form an equation in \( x \) to represent the above information and show that it can be transformed into \( 10x^2 - 33x + 20 = 0 \).
(b) Solve the equation in (a) to find the possible values of \( x \).

Solve the equation $$ \log_3 (x+4) + \log_3 (x-2) = \log_3 7 $$ for real values of $$x$$.