Chapter 8: Q. 1 (page 556)

Find the real solutions, if any, of the equation $3 x^{2} + 1 = 4 x$ .

Short Answer

Expert verified

The solutions of the equation are $x = \{\frac{1}{3}, 1\}$ .

Step by step solution

Step 1. Given Information

The given equation is $3 x^{2} + 1 = 4 x$ .

Step 2. Factor the Equation

Write the equation in standard form.

$3 x^{2} - 4 x + 1 = 0$

Factor the equations.

$\begin{array}{rcl} 3 x^{2} - 3 x - x + 1 & = & 0 \\ (3 x - 1) (x - 1) & = & 0 \end{array}$

Step 3. Find the Solution

Equate both the factors to 0 to find the solution.

$\begin{array}{rcl} 3 x - 1 & = & 0 \\ x & = & \frac{1}{3} \\ x - 1 & = & 0 \\ x & = & 1 \end{array}$

So, the solution set of $x$ isrole="math" localid="1646704327562" $\{\frac{1}{3}, 1\}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the real solutions, if any, of the equation $3 x^{2} + 1 = 4 x$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the Equation

Step 3. Find the Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Pure Maths

Discrete Mathematics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Find the real solutions, if any, of the equation 3x2+1=4x.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the Equation

Step 3. Find the Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Pure Maths

Discrete Mathematics

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Find the real solutions, if any, of the equation $3 x^{2} + 1 = 4 x$ .