What is the value of n so that the expression x² + 11x + n is a perfect square trinomial?

Solution:

Given, the expression is x² + 11x + n ------> (1)

A perfect square is an expression in the form (x + a)² which can be written in a trinomial form as

(x + a)² = (x + a)(x + a) = x² + ax + ax + a²

(x + a)² = x² + 2ax + a²------> (2)

Comparing (1) and (2)

2ax = 11x

2a = 11

a = 11/2

Also, a² = n

n = (11/2)² = 121/4

The expression is x² + 11x + 121/4.

Therefore, the value of n is 121/4.

What is the value of n so that the expression x² + 11x + n is a perfect square trinomial?

Summary:

The value of n so that the expression x² + 11x + n is a perfect square trinomial is 121/4.