Question

In the given problem, solve and graph. Express answers in both inequality and interval notaion.$x^2-1\ge 4x$

Answer 1

$x^2-1\ge 4x$

$x^2-1-4x\ge 0$

$x^2-1-4x=0$

$x=\frac{-(-4)\pm \sqrt{{(-4)}^2-4\cdot 1(-1)}}{2\cdot 1}:2\pm \sqrt{5}$

$(x-(2+\sqrt{5}))(x-(2-\sqrt{5}))\ge 0$

x< $2-\sqrt{5}$ x=$2-\sqrt{5}$ $2-\sqrt{5}<x<2+\sqrt{5}$ x=$2+\sqrt{5}$ x>$2+\sqrt{5}$ x-$(2+\sqrt{5})$ - - - 0 + x-$(2-\sqrt{5})$ - 0 + + + (x-$(2+\sqrt{5}$))(x-$(2+\sqrt{5}$)) + 0 - 0 +
					+

$\left[\begin{array}{cc}Solution:& x\le 2-\sqrt{5}orx\ge 2+\sqrt{5}\\ Decimal:& x\le -0.23607\dots orx\ge 4.23607\dots \\ IntervalNotation:& (-\infty ,2-\sqrt{5}]\cup [2+\sqrt{5},\infty )\end{array}\right]$