Chapter 7.4, Problem 11OE

To determine

For the equation , substitute z for some expression in x to make the equation easier to solve. Then give the resulting quadratic equation in z.

$2x^{-2}+3x^{-1}-2=0$

Answer to Problem 11OE

  $x^{-1}=z$

  $2z^2+3z-2=0$

Explanation of Solution

Given:

The equation is :

  $2x^{-2}+3x^{-1}-2=0$

Calculation:

Given:

  $\begin{array}{l}2x^{-2}+3x^{-1}-2=0\\ \Rightarrow 2{\left(x^{-1}\right)}^2+3\left(x^{-1}\right)-2=0\end{array}$

Substitute

$x^{-1}=z$

So, the resulting quadratic equation is :

  $\begin{array}{l}2x^{-2}+3x^{-1}-2=0\\ \Rightarrow 2{\left(x^{-1}\right)}^2+3\left(x^{-1}\right)-2=0\\ \Rightarrow 2z^2+3z-2=0\end{array}$