Q.176 In the following exercises, solv... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.176 (page 906)

In the following exercises, solve equations in Quadratic Form for $6 x 鈥� + 鈥� \sqrt{x} 鈥� 鈭� 鈥� 1 鈥� = 鈥� 0$ .

Short Answer

Expert verified

The solution of the quadratic equation is $x = \frac{1}{9}$ .

Step by step solution

Step 1. Given Information.

The given equation is $6 x 鈥� + 鈥� \sqrt{x} 鈥� 鈭� 鈥� 1 鈥� = 鈥� 0$ .

Step 2. Remove Square root

Solving $6 x 鈥� + 鈥� \sqrt{x} 鈥� 鈭� 鈥� 1 鈥� = 鈥� 0$

$6 x - 1 = - \sqrt{x}$

Squaring both sides , we get:-

${(6 x - 1)}^{2} = {(- \sqrt{x})}^{2} 36 x^{2} - 12 x + 1 = x 36 x^{2} - 12 x + 1 - x = 0 36 x^{2} - 13 x + 1 = 0$

Step 3. Solving using Quadratic equation.

Solving $36 x^{2} - 13 x + 1 = 0$

Using Quadratic formula:-

$\begin{array}{rcl} x_{1, 鈥� 2} & = & \frac{- (- 13) 卤 \sqrt{{(- 13)}^{2} - 4 路鈥� 36 路鈥� 1}}{2 路鈥� 36} \\ x_{1, 鈥� 2} & = & \frac{- (- 13) 卤鈥� 5}{2 路鈥� 36} \\ x_{1} & = & \frac{- (- 13) + 5}{2 路鈥� 36}, 鈥� x_{2} = \frac{- (- 13) - 5}{2 路鈥� 36} \\ x & = & \frac{1}{4}, 鈥� x = \frac{1}{9} \end{array}$

. Verifying the solution

Plug the value of $x = \frac{1}{4}$ in equation $6 x 鈥� + 鈥� \sqrt{x} 鈥� 鈭� 鈥� 1 鈥� = 鈥� 0$ we get:-

$\begin{array}{rcl} 6 (\frac{1}{4}) + \sqrt{\frac{1}{4}} - 1 & = & \frac{3}{2} + \frac{1}{2} - 1 \\ \frac{3}{2} + \frac{1}{2} - 1 & = & 2 - 1 \\ 2 - 1 & = & 1 \end{array}$

Similarly , Plug value of $x = \frac{1}{9}$ in equation $6 x 鈥� + 鈥� \sqrt{x} 鈥� 鈭� 鈥� 1 鈥� = 鈥� 0$ , we get:-

$6 (\frac{1}{9}) + 鈥� \sqrt{\frac{1}{9}} 鈥� 鈭� 鈥� 1 鈥� = 鈥� \frac{2}{3} + \frac{1}{3} - 1 \frac{2}{3} + \frac{1}{3} - 1 = \frac{3}{3} - 1 1 - 1 = 0$

Since, for the value of $x = \frac{1}{9}$ the equation satisfied the condition. Hence, The solution of the equation is $x = \frac{1}{9}$ .

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91影视

In the following exercises, solve equations in Quadratic Form for $6 x 鈥� + 鈥� \sqrt{x} 鈥� 鈭� 鈥� 1 鈥� = 鈥� 0$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove Square root

Step 3. Solving using Quadratic equation.

. Verifying the solution

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

In the following exercises, solve equations in Quadratic Form for 6x鈥�+鈥�x鈥�鈭�鈥�1鈥�=鈥�0.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove Square root

Step 3. Solving using Quadratic equation.

. Verifying the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Calculus

Statistics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve equations in Quadratic Form for $6 x 鈥� + 鈥� \sqrt{x} 鈥� 鈭� 鈥� 1 鈥� = 鈥� 0$ .