Which of the following equations has only one solution?
x² + 4x + 4 = 0, x² + x = 0, x² - 1 = 0

Solution:

To find which equation has only one solution, we will solve for x in each of the given equations.

Consider equation x² + x

Taking the common factor out,

⇒ x(x + 1) = 0

Using zero product rule.

x = 0, x = -1

Thus, this equation has two solutions.

x² + 4x + 4 = 0

Factorize the quadratic equation by splitting the middle term.

x² + 2x + 2x + 4 = 0

x(x + 2) + 2(x + 2) = 0

(x + 2)(x + 2) = 0

x = -2

Thus, this equation has only one solution.

⇒ x² - 1 = 0 or x² - (1)² 

⇒ (x + 1) (x - 1) [using the algebraic identity a² - b² = (a + b)(a - b)]

⇒ x = -1 or x = 1

Thus, this equation has two solutions.

x² + 4x + 4 = 0 has one solution x = -2.

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Which of the following equations has only one solution?

Summary:

The equation x² + 4x + 4 = 0 has only one solution x = -2.