Chapter 7: Q. 5 (page 464)

Find the real solutions of ${(2 x - 1)}^{2} - 3 (2 x - 1) - 4 = 0$

Short Answer

Expert verified

The solution set is $\{0, \frac{5}{2}\}$

Step by step solution

Step 1. Given Information

We have to find the real solutions of ${(2 x - 1)}^{2} - 3 (2 x - 1) - 4 = 0$

Step 2. For this equation, let u=2x-1, Then u2=(2x-1)2and the original equation, (2x-1)2-3(2x-1)-4=0 becomes u2-3u-4=0.

Now factor the equation.

In the equation, the multiply of first and last term is $4$ and the middle factor is $3 .$

Step 3. The possible factors are 1 and 4.

$u^{2} - (4 - 1) u - 4 = 0 u^{2} - 4 u + u - 4 = 0 u (u - 4) + 1 (u - 4) = 0 (u + 1) (u - 4) = 0$

Step 4. Now putting the value equal to zero.

$u + 1 = 0 u - 4 = 0 u + 1 - 1 = 0 - 1 u - 4 + 4 = 0 + 4 u = - 1 u = 4$

Step 5. But we want to solve for x. Because u=2x-1, we have

$2 x - 1 = - 1 2 x - 1 = 4 2 x - 1 + 1 = - 1 + 1 2 x - 1 + 1 = 4 + 1 2 x = 0 2 x = 5 x = 0 x = \frac{5}{2}$

The solution set is $\{0, \frac{5}{2}\} .$

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Find the real solutions of ${(2 x - 1)}^{2} - 3 (2 x - 1) - 4 = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. For this equation, let u=2x-1, Then u2=(2x-1)2and the original equation, (2x-1)2-3(2x-1)-4=0 becomes u2-3u-4=0.

Step 3. The possible factors are 1 and 4.

Step 4. Now putting the value equal to zero.

Step 5. But we want to solve for x. Because u=2x-1, we have

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Find the real solutions of(2x-1)2-3(2x-1)-4=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. For this equation, let u=2x-1, Then u2=(2x-1)2and the original equation, (2x-1)2-3(2x-1)-4=0 becomes u2-3u-4=0.

Step 3. The possible factors are 1 and 4.

Step 4. Now putting the value equal to zero.

Step 5. But we want to solve for x. Because u=2x-1, we have

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Geometry

Probability and Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the real solutions of ${(2 x - 1)}^{2} - 3 (2 x - 1) - 4 = 0$