Final answer:
To find the value of n such that x² - 3x + n is a perfect square trinomial, the constant term must be (3/2)² = 9/4. Therefore, the value of n is 9/4.
Step-by-step explanation:
To find the value of n such that x² - 3x + n is a perfect square trinomial, we need to consider the coefficient of the linear term (3x) and its relationship to the coefficient of the quadratic term (x²). In a perfect square trinomial, the linear term is twice the product of the square root of the quadratic term and the constant term. In this case, the square root of x² is x, and twice the product of x and the constant term is 3x. Therefore, the constant term must be (3/2)² = 9/4. Hence, the value of n is 9/4.
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