If x² + mx + m is a perfect-square trinomial, which equation must be true?
x² + mx + m = (x - 1)²
x² + mx + m = (x + 1)²
x² + mx + m = (x + 2)²
x² + mx + m = (x + 4)²

Solution:

A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression.

It is of the form ax² + bx + c.

Here a, b, and c are real numbers and a ≠ 0.

It is given that

x² + mx + m is a perfect-square trinomial

Its equation is

x² + mx + m = (x + 2)²

(x + 2)² = x² + 4x + 4

Therefore, x² + mx + m = (x + 2)² must be true.

If x² + mx + m is a perfect-square trinomial, which equation must be true?

Summary:

If x² + mx + m is a perfect-square trinomial, x² + mx + m = (x + 2)² must be true.