Chapter 11: Q. 192 (page 1069)

In the following exercises, solve.
$15 x^{- 2} - 4 x^{- 1} - 4 = 0$

Short Answer

Expert verified

The solutions of the given equation are $x = - \frac{5}{2}$ and $x = \frac{3}{2}$ .

Step by step solution

Step 1. Write the equation in standard form.

The given equation is:

$15 x^{- 2} - 4 x^{- 1} - 4 = 0$

It can be written as:

$15 (x^{- 1})^{2} - 4 x^{- 1} - 4 = 0$

Substitute $x^{- 1} = u$ .

role="math" localid="1644992521952" $15 u^{2} - 4 u - 4 = 0$

Step 2. Solve the equation.

Split the middle term.

$\begin{array}{rcl} 15 u^{2} - 10 u + 6 u - 4 & = & 0 \\ 5 u (3 u - 2) + 2 (3 u - 2) & = & 0 \\ (5 u + 2) (3 u - 2) & = & 0 \\ u & = & - \frac{2}{5} and u = \frac{2}{3} \end{array}$

Substitute $u = x^{- 1}$ .

$\begin{array}{rcl} x^{- 1} & = & - \frac{2}{5} and x^{- 1} = \frac{2}{3} \\ x & = & - \frac{5}{2} and x = \frac{3}{2} \end{array}$

Step 3. Conclusion.

The solutions of the given equation are $- \frac{5}{2}$ and $x = \frac{3}{2}$ .

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In the following exercises, solve.
$15 x^{- 2} - 4 x^{- 1} - 4 = 0$

Short Answer

Step by step solution

Step 1. Write the equation in standard form.

Step 2. Solve the equation.

Step 3. Conclusion.

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In the following exercises, solve.15x-2-4x-1-4=0

Short Answer

Step by step solution

Step 1. Write the equation in standard form.

Step 2. Solve the equation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$15 x^{- 2} - 4 x^{- 1} - 4 = 0$