Chapter 5: Q. 36 (page 349)

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility: $3^{x^{2} + x} = \sqrt{3}$

Short Answer

Expert verified

The solution set of $x = \{\frac{- 1 - \sqrt{3}}{2}, \frac{- 1 + \sqrt{3}}{2}\} \approx \{- 1.366, 0.366\}$

Step by step solution

Step 1. Given information

An equation, $3^{x^{2} + x} = \sqrt{3}$

Step 2. Required to find

Solve the given equation to find x.

Step 3. Solving the equation

Given, $3^{x^{2} + x} = \sqrt{3}$

role="math" localid="1646572989517" $\Rightarrow 3^{x^{2} + x} = 3^{\frac{1}{2}}$

$\Rightarrow x^{2} + x = \frac{1}{2}$

$\Rightarrow x^{2} + x - 0.5 = 0$

For quadratic equation, $a x^{2} + b x + c = 0$ , using quadratic formula, $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$x = \frac{- 1 \pm \sqrt{1^{2} - 4 (1) (- 0.5)}}{2 (1)}$

$x = \frac{- 1 \pm \sqrt{1 + 2}}{2}$

$x = \frac{- 1 \pm \sqrt{3}}{2}$

role="math" localid="1646573703954" $x = \frac{- 1 - \sqrt{3}}{2}, x = \frac{- 1 + \sqrt{3}}{2}$

$x = - 1.366, x = 0.366$

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Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility: $3^{x^{2} + x} = \sqrt{3}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Required to find

Step 3. Solving the equation

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Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility:3x2+x=3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Required to find

Step 3. Solving the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility: $3^{x^{2} + x} = \sqrt{3}$