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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.68 (page 905)

Solve :- $6 x^{- 2} - 23 x^{- 1} + 20 = 0$

Short Answer

Expert verified

Solution for Equation will be -

$x = \frac{2}{5}$
$x = \frac{3}{4}$

Step by step solution

01

Step 1. Given Data

Quadratic Equation - $6 x^{- 2} - 23 x^{- 1} + 20 = 0$

02

Step 2. To Find

We have to solve it and find the value of x.

03

Step 3. Explanation

Let the value of $x^{- 1} = u$

Then the equation is -

$6 x^{- 2} - 23 x^{- 1} + 20 = 0$

role="math" localid="1645031655392" ${6 (x^{- 1})}^{2} - 23 x^{- 1} + 20 = 0$

Put the value of $x^{- 1} = u$

$6 u^{2} - 23 u + 20 = 0$

$(u - \frac{5}{2}) (u - \frac{4}{3}) = 0$

By using zero product property -

$u - \frac{5}{2} = 0$ , $u - \frac{4}{3} = 0$

04

Step 4. Calculation

Replace u with $x^{- 1}$

$x^{- 1} = \frac{5}{2}$ , $x^{- 1} = \frac{4}{3}$

Solve for x by taking the reciprocal since $x^{- 1} = \frac{1}{x}$

$x = \frac{2}{5}$ , $x = \frac{3}{4}$

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