Equations-and-inequalities

Question 1

$1.1$ Solve for $x$ :
$\quad 1.1.1$	$x^2-6x=0$	$(2)$
$\quad 1.1.2$	$x^2+10x+8=0\quad$ (correct to TWO decimal places)	$(3)$
$\quad 1.1.3$	$(1-x)(x+2)<0$	$(3)$
$\quad 1.1.4$	$\sqrt{x+18}=x-2$	$(5)$
$1.2$	Solve simultaneously for $x$ and $y$ : $x+y=3\;$ and $\;2x^2+4xy-y=15$	$(6)$

$1.3$	If $n$ is the largest integer for which $n^{200}<5^{300}$ , determine the value of $n$ .	$(3)$
		$\textbf{[22]}$

$1.1$ Solve for $x$ :
$\quad 1.1.1$	$x^2+5x-6=0$	$(3)$
$\quad 1.1.2$	$4x^2+3x-5=0\quad$ (correct to TWO decimal places)	$(3)$
$\quad 1.1.3$	$4x^2-1<0$	$(3)$
$\quad 1.1.4$	$(\sqrt{\sqrt{32}+x})(\sqrt{\sqrt{32}-x})=x$	$(4)$
$1.2$	Solve simultaneously for $x$ and $y$ : $y+x=12\;$ and $\;xy=14-3x$	$(5)$

$1.3$	Consider the product $1 \times 2 \times 3 \times 4 \times \cdots \times 30$ . Determine the largest value of $k$ such that $3^k$ is a factor of this product.	$(4)$

		$\textbf{[22]}$