Los de volgende vergelijkingen exact op:
a. $$\frac{1}{2}x^2 - 4 = 4$$
b. $$36x^2 - 10 = 15$$
c. $$\frac{1}{2}x^2 + 1 = 15$$
Uitwerking:
a. $$\frac{1}{2}x^2 - 4 = 4$$
$$\frac{1}{2}x^2 = 8 $$
$$x^2 = 8 · 2$$
$$x^2 = 16$$
$$x = \sqrt{16}$$
x = 4 of x = -4
b. $$36x^2 - 10 = 15$$
$$36x^2 = 25$$
$$x^2 = \frac{25}{36}$$
$$x = \sqrt{\frac{25}{36}} \vee x = -\sqrt{\frac{25}{36}}$$
$$x = \frac{5}{6} \vee x = -\frac{5}{6}$$
c. $$\frac{1}{2}x^2 + 1 = 15$$
$$\frac{1}{2}x^2 = 14$$
$$x^2 = 14 · 2 $$
$$x^2 = 28$$
$$x = \sqrt{28} \vee -\sqrt{28}$$
$$\sqrt{28} = \sqrt{4} · \sqrt{7} = 2\sqrt{7}$$
$$ x = 2\sqrt{7} \vee x = -2\sqrt{7}$$