Which of the following constants can be added to x2 - 6x to form a perfect square trinomial?
6, 9, 36, None of the above

Solution:

A perfect square trinomial is of the form

(a - b)² = a² - 2ab + b² --- (1)

Given, the equation is x² - 6x + __

Let us take the missing term as c,

now, x² - 6x + c --- (2)

Comparing (1) and (2), we get,

⇒ a² = x²

⇒ a = x

⇒ -2ab = - 6x

We know, a = x

So, -2xb = -6x

⇒ 2b = 6

⇒ b = 6/2

⇒ b = 3

⇒ b² = c

⇒ c = 3²

⇒ c = 9

Therefore, the constant to be added is 9.

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Which of the following constants can be added to x² - 6x to form a perfect square trinomial?

Summary:

The constant to be added to x² - 6x to form a perfect square trinomial is 9.