Question

what number is added to x² + 6x to get a perfect square ?​

Answer 1

Answer:

3 is the correct answer

Step-by-step explanation:

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Answer 2

Answer:

9 needs to be added to x2 - 6x to make it a perfect square.

Step-by-step explanation:

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.

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