Chapter 11: Q.178 (page 1069)

In the following exercises, solve equations in Quadratic Form for $12 x + 5 \sqrt{x} - 3 = 0$ .

Short Answer

Expert verified

The solution of the quadratic equation is $x = \frac{9}{16}, x = \frac{1}{9}$ .

Step by step solution

Step 1. Given Information.

The given equation is $12 x + 5 \sqrt{x} - 3 = 0$ .

Step 2. Remove Square root

Solving $12 x + 5 \sqrt{x} - 3 = 0$

${(12 x - 3)}^{2} = {(- 5 \sqrt{x})}^{2} 144 x^{2} - 72 x + 9 = 25 x 144 x^{2} - 72 x - 25 x + 9 = 0 144 x^{2} - 97 x + 9 = 0$

Step 3. Solving using Quadratic equation.

Solving $144 x^{2} - 97 x + 9 = 0$

$\begin{array}{rcl} x_{1, 2} & = & \frac{- (- 97) \pm \sqrt{{(- 97)}^{2} - 4 \cdot 144 \cdot 9}}{2 \cdot 144} \\ x_{1, 2} & = & \frac{- (- 97) \pm 65}{2 \cdot 144} \\ x_{1} & = & \frac{- (- 97) + 65}{2 \cdot 144}, x_{2} = \frac{- (- 97) - 65}{2 \cdot 144} \\ x & = & \frac{9}{16}, x = \frac{1}{9} \end{array}$

. Verifying the solution

Plug the value of $x = \frac{9}{16}$ in equation $12 x + 5 \sqrt{x} - 3 = 0$ , we get:-

$\begin{array}{rcl} 12 (\frac{9}{16}) + 5 \sqrt{\frac{9}{16}} - 3 & = & \frac{27}{4} + \frac{15}{4} - 3 \\ \frac{27}{4} + \frac{15}{4} - 3 & = & \frac{42}{4} - 3 \\ \frac{42}{4} - 3 & = & \frac{30}{4} \\ \frac{30}{4} & = & \frac{15}{2} \end{array}$

Since the value of $\frac{9}{16}$ is the equation satisfied the condition.

Similarly, Plug value of $x = \frac{1}{9}$ in equation $12 x + 5 \sqrt{x} - 3 = 0$ , we get:-

localid="1645292125046" $\begin{array}{rcl} 12 (\frac{1}{9}) + 5 \sqrt{\frac{1}{9}} - 3 & = & \frac{4}{3} + \frac{5}{3} - 3 \\ \frac{4}{3} + \frac{5}{3} - 3 & = & \frac{9}{3} - 3 \\ \frac{9}{3} - 3 & = & 3 - 3 \\ 3 - 3 & = & 0 \end{array}$

Since the value of $x = \frac{1}{9}$ the equation satisfied the condition.

Hence, The solution of the equation is localid="1663940752402" $x = \frac{9}{16}, x = \frac{1}{9}$ .

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In the following exercises, solve equations in Quadratic Form for $12 x + 5 \sqrt{x} - 3 = 0$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove Square root

Step 3. Solving using Quadratic equation.

. Verifying the solution

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In the following exercises, solve equations in Quadratic Form for 12x + 5x − 3 = 0.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove Square root

Step 3. Solving using Quadratic equation.

. Verifying the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve equations in Quadratic Form for $12 x + 5 \sqrt{x} - 3 = 0$ .