Let's solve each problem step-by-step:

Question 1

1. Solve the equations:

1. $(x^2 - 169) / x^2 = 0$

To solve the equation $\frac{x^2 - 169}{x^2} = 0$, we start by setting the numerator equal to zero because a fraction equals zero if and only if its numerator is zero (and the denominator is non-zero).

$x^2 - 169 = 0$

This is a difference of squares, so we can factor it:

$(x - 13)(x + 13) = 0$

Setting each factor equal to zero gives us:

$x - 13 = 0 \quad \text{or} \quad x + 13 = 0$ $x = 13 \quad \text{or} \quad x = -13$

So, the solutions are $x = 13$ and $x = -13$.

2. $2x^2 - 7x + 6 = 0$ (use the quadratic formula)

The quadratic formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For the equation $2x^2 - 7x + 6 = 0$, the coefficients are $a = 2$, $b = -7$, and $c = 6$.

First, we calculate the discriminant:

$b^2 - 4ac = (-7)^2 - 4(2)(6) = 49 - 48 = 1$

Now, apply the quadratic formula:

$x = \frac{-(-7) \pm \sqrt{1}}{2(2)}$ $x = \frac{7 \pm 1}{4}$

This gives us two solutions:

$x = \frac{7 + 1}{4} = \frac{8}{4} = 2$ $x = \frac{7 - 1}{4} = \frac{6}{4} = \frac{3}{2}$

So, the solutions are $x = 2$ and $x = \frac{3}{2}$.