Question

2.

What extraneous solution arises when the equation x + 3 = 2x is solved for
x by first squaring both sides of the equation?
Enter your answer in the box.

Answer 1

When the equation x+3=2x is incorrectly solved by first squaring both sides, an extraneous solution may be introduced due to unnecessary squaring of a linear equation.

Step-by-step explanation:

When addressing the equation x + 3 = 2x, and solving for x by first squaring both sides of the equation, an extraneous solution may arise. To find this solution, you would take the following steps:

Square both sides: (x + 3)2 = (2x)2.

Expand both sides: x2 + 6x + 9 = 4x2.

Rearrange to form a quadratic equation: 0 = 4x2 - x2 - 6x - 9.

Simplify: 0 = 3x2 - 6x - 9.

Find the solutions using the quadratic formula or by factoring.

However, the original equation is a linear one, and such process of squaring should not introduce new solutions if done correctly. Yet, due to the squaring, we may inadvertently create an extraneous solution that does not satisfy the original equation.

Answer 2

x = -3/4

Step-by-step explanation:

I assume the question is

√(x + 3) = 2x

Square both sides.

x + 3 = 4x²

4x² - x - 3 = 0

(4x + 3)(x - 1) = 0

4x + 3 = 0 or x - 1 = 0

x = -3/4 or x = 1

Check solution x = -3/4 in the original equation.

√(x + 3) = 2x

√(-3/4 + 3) = 2(-3/4)

This solution cannot work since the right side is negative, and a square root cannot equal a negative number.

Check solution x = 1 in the original equation.

√(x + 3) = 2x

√(1 + 3) = 2(1)

√4 = 2

2 = 2

Solution x = 1 works.

Answer: x = -3/4