Chapter 9: Q. 9.160 (page 1099)

Solve: $\sqrt{n + 1} - n + 1 = 0$ .

Short Answer

Expert verified

The solution is $n = 3$ .

Step by step solution

Step 1. Given Information

We are given the quadratic equation $\sqrt{n + 1} - n + 1 = 0$ and we need to solve it.

Step 2. Finding the solution

Isolating the radical on one side of the equation:

$\sqrt{n + 1} - n + 1 = 0 \Rightarrow \sqrt{n + 1} = n - 1$

Squaring both sides of the equation, we get:

${(\sqrt{n + 1})}^{2} = {(n - 1)}^{2} \Rightarrow n + 1 = n^{2} - 2 n + 1 \Rightarrow n^{2} - 2 n + 1 - n - 1 = 0 \Rightarrow n^{2} - 3 n = 0 \Rightarrow n (n - 3) = 0$

Using the zero product property, we get:

$n = 0, (n - 3) = 0 \Rightarrow n = 3$

Step 3. Checking the answer

$n = 0, \sqrt{n + 1} - n + 1 = 0 \Rightarrow \sqrt{0 + 1} - 0 + 1 = 0 \Rightarrow \sqrt{1} + 1 = 0 \Rightarrow 2 \neq 0 n = 3, \sqrt{n + 1} - n + 1 = 0 \Rightarrow \sqrt{3 + 1} - 3 + 1 = 0 \Rightarrow \sqrt{4} - 2 = 0 \Rightarrow 2 - 2 = 0 \Rightarrow 0 = 0$

$n = 0$ is an extraneous solution.

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Solve: $\sqrt{n + 1} - n + 1 = 0$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the solution

Step 3. Checking the answer

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Solve:n+1-n+1=0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the solution

Step 3. Checking the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve: $\sqrt{n + 1} - n + 1 = 0$ .