Chapter 9: Q. 9.10 (page 864)

Solve $3 t^{2} + 6 = 70$

Short Answer

Expert verified

The solutions are $t = \frac{8 \sqrt{3}}{3}, t = - \frac{8 \sqrt{3}}{3}$

Step by step solution

Step 1. Given information

Consider the quadratic equation

$3 t^{2} + 6 = 70$

The objective is to solve the quadratic equation by using square root property.

If $x^{2} = k$ , then $x = \pm \sqrt{k}$

Isolate the quadratic term.

$3 t^{2} = 64$

Divide by 3 to make the coefficient 1.

$\frac{3 t^{2}}{3} = \frac{64}{3} t^{2} = \frac{64}{3}$

Use the Square Root Property.

$t = \pm \sqrt{\frac{64}{3}}$

Step 2. Simplify the radical expression.

Rewrite the radical as a fraction of square roots.

$t = \pm \frac{\sqrt{64}}{\sqrt{3}}$

Rationalize the denominator.

$t = \pm \frac{\sqrt{64}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} t = \pm \frac{8 \sqrt{3}}{3}$

Rewrite to show two solutions.

$t = \frac{8 \sqrt{3}}{3}, t = - \frac{8 \sqrt{3}}{3}$

Step 3. Check the solutions:

Substitute $t = \frac{8 \sqrt{3}}{3}$ in the original equation.

role="math" localid="1645373895892" $3 t^{2} + 6 = 70 3 {(\frac{8 \sqrt{3}}{3})}^{2} + 6 \overset{?}{=} 70 3 (\frac{64 \cdot 3}{9}) + 6 \overset{?}{=} 70 64 + 6 \overset{?}{=} 70 70 = 70$

Substitute $t = \frac{8 \sqrt{3}}{3}$ in the original equation.

$3 t^{2} + 6 = 70 3 {(- \frac{8 \sqrt{3}}{3})}^{2} + 6 \overset{?}{=} 70 3 (\frac{64 \cdot 3}{9}) + 6 \overset{?}{=} 70 64 + 6 \overset{?}{=} 70 70 = 70$

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Solve $3 t^{2} + 6 = 70$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the radical expression.

Step 3. Check the solutions:

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Solve3t2+6=70

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the radical expression.

Step 3. Check the solutions:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Geometry

Decision Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve $3 t^{2} + 6 = 70$