Question

Solve the following expression for x. What is(are) the value(s) of the positive root(s)?

Answer 1

To solve (2x)² = 4.0 (1 − x)², we take the square root of both sides and rearrange the equation to solve for x, resulting in two possible roots, x = 0 and x = 1. Since only positive roots are of interest, the solution is x = 1.

Step-by-step explanation:

To solve the expression (2x)² = 4.0 (1 − x)² for x, we identify that this equation involves perfect squares on both sides. Taking the square root of both sides, we get (2x) (1 − x). Let's proceed with the steps to solve for x:

1. First, expand (2x)(1 - x) to get 2x - 2x².
2. Next, rearrange the equation to set it to zero: 2x² - 2x = 0.
3. Factor out the common term: 2x(x - 1) = 0.
4. Set each factor equal to zero: x = 0 and x - 1 = 0.
5. Solving these gives two possible roots: x = 0 and x = 1.
6. Since we are only interested in the positive root, the answer is x = 1.

It is important to understand the context of a problem. For instance, in Example 7.4, only the positive root was kept because negative speed is not feasible in a physical context. However, in some contexts like chemistry, negative concentrations are not possible, leading to the dismissal of negative roots for concentration calculations.