Los op vir $x$: 1.1.1 $(3x-6)(x+2)=0$ 1.1.2 $2x^2-6x+1=0$ (korrek tot TWEWE desimale plekke) 1.1.3 $x^2-90>x$ 1.1.4 $x-rac{7}{ oot{x}{2}}=-12$ Los gelijktydig vir $x$ en $y$ op: $2x-y=2$ $xy=4$ - NSC Mathematics - Question 1 - 2022 - Paper 1

Using the quadratic formula, where $a = 2$, $b = -6$, and $c = 1$:

oot{b^2 - 4ac}{2a}}$$ Calculating the discriminant: $$b^2 - 4ac = (-6)^2 - 4(2)(1) = 36 - 8 = 28$$ Now substituting into the quadratic formula: $$x = rac{6 ext{±} oot{28}{4}}{4} = rac{6 ext{±} 2 oot{7}}{4} = rac{3 ext{±} oot{7}}{2}$$ Calculating the two values: - $x eq 2,82$ - $x eq 0,18$

Rearranging the inequality gives:

$x^2 - x - 90 > 0$

Factoring:

$(x - 10)(x + 9) > 0$

The critical values are $x = 10$ and $x = -9$. The solution to the inequality is:

$x < -9 ext{ or } x > 10$

First, isolate $oot{x}{2}$:

oot{x}{2}}$$ Squaring both sides results in: $$x^2 + 24x + 144 = 49$$ So we have: $$x^2 + 24x + 95 = 0$$ Using the quadratic formula: $$x = rac{-24 ext{±} oot{24^2 - 4 imes 1 imes 95}{2 imes 1}}$$ Calculating yields: - $x = 9 ext{ or } x = -16$

We start with the equations:

1. $2x - y = 2$ (Eq 1)
2. $xy = 4$ (Eq 2)

From Eq 1, express $y$:

$y = 2x - 2$

Substituting into Eq 2:

$x(2x - 2) = 4$

This simplifies to:

$2x^2 - 2x - 4 = 0$

Dividing through by 2 gives:

$x^2 - x - 2 = 0$

Factoring:

$(x - 2)(x + 1) = 0$

So $x = 2 ext{ or } x = -1$.

Substituting back:

• For $x = 2$, $y = 2(2) - 2 = 2$
• For $x = -1$, $y = 2(-1) - 2 = -4$

Thus, the pairs are $(2, 2)$ and $(-1, -4)$.