step 1 For exercise 24, we have the factor form x times x minus 3 equals 0. From here, it's evident tha

Question

Solve: $(x-3)^{2}>0$

Name: Problem 99, Chapter 4: College Algebra
Uploaded: 2022-02-09T19:21:15-08:00
Duration: 35 s
Channel: Victor Salazar
Description: Solve: (x-3)^2>0

   Solve: $(x-3)^{2}>0$

College Algebra

Robert Blitzer 7th Edition

Chapter 4, Problem 99

Instant Answer

Solved by Expert Victor Salazar

02/09/2022

Step 1

This can be written as: \[ (x-3)^2 = (x-3)(x-3) = x^2 - 6x + 9 \] Show more…

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Solve: $(x-3)^{2}>0$

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Key Concepts

Solving Inequalities Involving Squared Expressions

When solving an inequality that involves a squared term, the key step is to recognize that the squared expression is zero at specific points and positive elsewhere. In the case of a strict inequality (greater than 0), the solution excludes the point where the expression equals zero, because that is the only situation where the square is not positive.

Properties of Squaring Real Numbers

Understanding that the square of any real number is always nonnegative is fundamental. This means for any real number a, the value of a² is at least 0, and it is exactly 0 only when a is 0. This property helps in determining how a squared term behaves in an inequality.

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