True or False ? Please Justify/ Explain you answer . 10 points best answer?

(generally) there are 3 types of statements.

1)  TRUE statement

2)  FALSE statement

3)  OPEN statement

For example, a FALSE statement would be

         x + 1 = x - 4

because you know that it is FALSE for any

value of x, since when you subtract x from

both sides you a statement    " 1 = -4 "

and thus you know that it is for sure FALSE.

A TRUE statement would, for example be,

         g² + 3 = g² + 3

since you see that what is basically says is,

" a number = a number ", and you know that

it is true, just like  1=1  r=r   3=3  -6=-6

and on...   is true, (right?)

In other words, whatever number you plug in

for g  into      g² + 3 = g² + 3,   the sides will

always be equal to each other.

An OPEN statement however, would be something like,

        w + 3 = 2w - 1

Here, you get a statement that is OPEN,

because you can solve the equation and

find what "w" equals.

Solution:

        w + 3 = 2w - 1      

   add 1 to both sides

        w + 3 = 2w - 1      

            + 1         + 1

      ───────────

        w + 4 = 2w

(the 1 on the right side has canceled)

Now, subtract w from both sides

        w + 4 = 2w      

      - w         - w

      ───────────

         4 = w

and hence, you know that

        w + 3 = 2w - 1      

is true when  w  is 4

but false for any other values.

This statement, that can be solved for the variable

to find what the variable equals (to make the statement true)

is called an OPEN statement.

You're not making much sense. Statements are true or false. Questions are not true or false.

"Is (X +2)^3 = x^3 -4 a quadratic equation?" is a question not a statement. Therefore it makes no sense to ask if it is true or false.

(X +2)^3 = x^3 -4 is a quadratic equation because it can be written in the form ax^2+bx+c = 0.

no

(x + 2)^3 = (x + 2)(x + 2)(x + 2)

= (x + 2)(x^2 + 4x + 4)

= x^3 + 6x^2 + 12x + 8

in general this is not the same as x^3 - 4

therefore false

no

(x + 2)^3 = (x + 2)(x + 2)(x + 2)

= (x + 2)(x^2 + 4x + 4)

= x^3 + 6x^2 + 12x + 8

in general this is not the same as x^3 - 4

it may be the same if 6x^2 + 12x + 8 = -4

or 6x^2 + 12x + 12 = 0

=> x^2 + 2x + 2 = 0

=> (x + 1)^2 = -1

=> x + 1 = ±i

=> x = -1 ± i

(x+2)² = x³-4

x²+4x+4 = x³-4

x³-x²-4x-8 = 0

This is a cubic equation.

Drop the course