Chapter 4.8, Problem 39PPS

To determine

To Find: The solution of the inequality algebraically

Answer to Problem 39PPS

  $\frac{\sqrt{10}}{2}or-\frac{\sqrt{10}}{2}$

Explanation of Solution

Given:

  $2x^2+4\ge 9$

Formula Used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using factorization method.

Calculation:

  $\begin{array}{l}2x^2+4\ge 9\\ \Rightarrow 2x^2-5\ge 0\\ a=2;\\ b=0;\\ c=-5\\ x=\frac{-0\pm \sqrt{{\left(0\right)}^2-4\left(2\right)\left(-5\right)}}{2\left(2\right)}\\ \Rightarrow x=\frac{0\pm \sqrt{0+40}}{4}\\ \Rightarrow x=\frac{0\pm 2\sqrt{10}}{4}\\ \Rightarrow x=\frac{\pm \sqrt{10}}{2}\\ \Rightarrow x=\frac{\sqrt{10}}{2}or-\frac{\sqrt{10}}{2}\end{array}$