Chapter 12: Q50. (page 637)

Solve each equation.
$\sqrt{x} + \sqrt{x + 5} = 5$

Short Answer

Expert verified

The solution is $x = 4$ .

Step by step solution

Step 1. Given Information.

Given, to solve the equation $\sqrt{x} + \sqrt{x + 5} = 5$ .

Step 2. Calculation.

Simplifying the equation:

$\begin{array}{l} \sqrt{x} + \sqrt{x + 5} = 5 \\ {(\sqrt{x} + \sqrt{x + 5})}^{2} = {(5)}^{2} \\ (x) + 2 (\sqrt{x}) (\sqrt{x + 5}) + (x + 5) = 25 \\ 2 \sqrt{x (x + 5)} = 25 - 5 - 2 x \\ 2 \sqrt{x (x + 5)} = 20 - 2 x \\ \sqrt{x (x + 5)} = 10 - x \\ {(\sqrt{x (x + 5)})}^{2} = {(10 - x)}^{2} \\ x^{2} + 5 x = 100 - 20 x + x^{2} \\ 5 x + 20 x = 100 \\ 25 x = 100 \\ x = 4 \end{array}$

Checking if the value of x satisfies the equation:

$\begin{array}{l} \sqrt{x} + \sqrt{x + 5} = 5 \\ \sqrt{4} + \sqrt{4 + 5} = 5 \\ \sqrt{4} + \sqrt{9} = 5 \\ 2 + 3 = 5 \\ 5 = 5 \end{array}$

Hence the value of x satisfies the equation.

Step 3. Conclusion.

Hence, the solution is x=4.

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Solve each equation.
$\sqrt{x} + \sqrt{x + 5} = 5$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Solve each equation.x+x+5=5

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Discrete Mathematics

Pure Maths

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Solve each equation.
$\sqrt{x} + \sqrt{x + 5} = 5$