3.If  (x + 1)2 + 1(x + 1)(x + 2) − (x − 1)  =  0 . Then the value of  4x2 + 8x + 9

The given equation is (x + 1)^2 + 1(x + 1)(x + 2) - (x - 1) = 0.

Let's simplify this equation step by step:

Step 1: Expand the terms = x^2 + 2x + 1 + x^2 + 3x + 2 - x + 1 = 0 = 2x^2 + 4x + 4 = 0

Step 2: Divide the entire equation by 2 to simplify = x^2 + 2x + 2 = 0

This is the simplified form of the given equation.

Now, we need to find the value of 4x^2 + 8x + 9.

Since we know that x^2 + 2x + 2 = 0, we can multiply the entire equation by 4 to get an equation in the form of 4x^2 + 8x + 8 = 0.

But we need to find the value of 4x^2 + 8x + 9.

Since 4x^2 + 8x + 8 = 0, adding 1 to both sides of the equation gives us 4x^2 + 8x + 9 = 1.

So, the value of 4x^2 + 8x + 9 is 1.