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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.8 (page 864)

Solve $\frac{3}{4} y^{2} - 3 = 18$

Short Answer

Expert verified

The solutions of the quadratic equation: $y = 2 \sqrt{7}, y = - 2 \sqrt{7}$

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

$\frac{3}{4} y^{2} - 3 = 18$

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

If $x^{2} = k$ , then $\frac{3}{4} y^{2} - 3 = 18$

Isolate the quadratic term.

$\frac{3}{4} y^{2} = 18 + 3 \frac{3}{4} y^{2} = 21$

Multiply by $\frac{4}{3}$ to make the coefficient 1.

localid="1645365650920" $\frac{4}{3} 路 \frac{3}{4} y^{2} = \frac{4}{3} 路 21 y^{2} = 28$

Use the Square Root Property.

localid="1645365679482" $y = 卤 \sqrt{28}$

02

Step 2. Simplify the expression.

Simplify the radical.

$y = 卤 \sqrt{4 路 7} y = 卤 2 \sqrt{7}$

Rewrite to show two solutions.

$y = 2 \sqrt{7}, y = - 2 \sqrt{7}$

03

Step 3. Check the solutions:

Substitute $y = 2 \sqrt{7}$ in the original equation.

$\frac{3}{4} y^{2} - 3 = 18 \frac{3}{4} {(2 \sqrt{7})}^{2} - 3 \overset{?}{=} 18 \frac{3}{4} (28) - 3 \overset{?}{=} 18 18 = 18$

And substitute role="math" localid="1645366022939" $y = - 2 \sqrt{7}$ in the original equation.

$\frac{3}{4} y^{2} - 3 = 18 \frac{3}{4} {(- 2 \sqrt{7})}^{2} - 3 \overset{?}{=} 18 \frac{3}{4} (28) - 3 \overset{?}{=} 18 18 = 18$

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