Chapter 9: Q.188 (page 906)

In the following exercises, solve equations in Quadratic Form for $2 x - 7 x^{\frac{1}{2}} = 15$ .

Short Answer

Expert verified

The solution of the quadratic equation is $x = 25$ .

Step by step solution

Step 1. Given Information.

The given equation is $2 x - 7 x^{\frac{1}{2}} = 15$ .

Step 2. Remove square roots

Simplify $2 x - 7 x^{\frac{1}{2}} = 15 2 x - 15 = 7 x^{\frac{1}{2}}$

Squaring both sides , we get:-

${(2 x - 15)}^{2} = {(7 x^{\frac{1}{2}})}^{2} 225 - 60 x + 4 x^{2} = 49 x 4 x^{2} - 60 x - 49 x + 225 = 0 4 x^{2} - 109 x + 225 = 0$

Step 3. Solving quadratic equation .

Using Quadratic formula :-

$x_{1, 2} = \frac{- (- 109) \pm \sqrt{{(- 109)}^{2} - 4 \cdot 4 \cdot 225}}{2 \cdot 4} x_{1, 2} = \frac{- (- 109) \pm 91}{2 \cdot 4} x_{1} = \frac{- (- 109) + 91}{2 \cdot 4}, x_{2} = \frac{- (- 109) - 91}{2 \cdot 4} x = 25, x = \frac{9}{4}$

Step 4. Verifying the Solution.

Substitute the value of $x = 25$ in equation $2 x - 7 x^{\frac{1}{2}} - 15 = 0$ , we get:-

$2 (25) - 7 {(25)}^{\frac{1}{2}} - 15 = 50 - 35 - 15 50 - 35 - 15 = 0$

Similarly , Substitute the value of $x = \frac{9}{4}$ in the equation $2 x - 7 x^{\frac{1}{2}} - 15 = 0$ , we get:-

role="math" localid="1645356098661" $2 (\frac{9}{4}) - 7 {(\frac{9}{4})}^{\frac{1}{2}} - 15 = \frac{9}{2} - \frac{21}{2} - 15 \frac{9}{2} - \frac{21}{2} - 15 = \frac{- 12}{2} - 15 \frac{- 12}{2} - 15 = - 6 - 15 - 6 - 15 = - 21 - 21 \neq 0$

Since, The condition for $x = 25$ is verified. Therefore, The solution of the equation is $x = 25$ .

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In the following exercises, solve equations in Quadratic Form for $2 x - 7 x^{\frac{1}{2}} = 15$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove square roots

Step 3. Solving quadratic equation .

Step 4. Verifying the Solution.

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In the following exercises, solve equations in Quadratic Form for 2x − 7x12= 15.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Remove square roots

Step 3. Solving quadratic equation .

Step 4. Verifying the Solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Statistics

Theoretical and Mathematical Physics

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Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve equations in Quadratic Form for $2 x - 7 x^{\frac{1}{2}} = 15$ .