> #mathematics > The expression 9x^2+12x+1+C where C is a constant is a perfect square. Find the value of C ?
Aug 4

# The expression 9x^2+12x+1+C where C is a constant is a perfect square. Find the value of C ?

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Aug 4
To determine if the expression is a perfect square, we need to factor the quadratic expression.

The given expression is 9x^2 + 12x + 1 + C

We can rewrite this expression as (3x + 1)^2 + C

Expanding (3x + 1)^2, we get 9x^2 + 6x + 1

Comparing this with the given expression, we see that C = 1

Therefore, the value of C is 1.
-1
Aug 4
Step 1: Identify the pattern of a perfect square trinomial.

A perfect square trinomial has the following form:

```
(ax + b)^2 = a^2x^2 + 2abx + b^2
```

Step 2: Compare the given expression to the perfect square trinomial form.

```
9x^2 + 12x + 1 = ?
```

Step 3: Equate the coefficients of the terms.

```
a^2 = 9
2ab = 12
b^2 = 1
```

Step 4: Solve for the coefficients a and b.

```
a = 3 (since 9 is a perfect square of 3)
b = 2 (since 12 = 2 - 3 - 2)
```

Step 5: Calculate the constant C.

```
C = b^2 = 2^2 = 4
```

Therefore, the value of C is 4.
-1
Anonymous
Aug 4
C=3
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