What constant can be added to x2 - 6x to form a perfect square trinomial?
A perfect square is an expression that can be expressed as a square of a real number.
Answer: 9 needs to be added to x2 - 6x to make it a perfect square.
Let's look into the steps below.
Given expression: x2 - 6x
To find the perfect square, we need to add a constant value to this expression to get the form of (a - b)2.
Let the constant value added be c.
Thus, the expression becomes: x2 - 6x + c
We know the algebraic identity, (a - b)2 = a2 - 2ab + b2
On comparing x2 - 6x + c with a2 - 2ab + b2 we get,
a2 = x2
Thus, a = x
Also, b2 = c and -2ab = -6x
-2xb = -6x [Since, a = x]
Dividing both the sides by -2x, we get,
b = 3
Therefore, c = b2 = 32 = 9.
Thus, 9 needs to be added to x2 - 6x to make it a perfect square.