Is the following statement true:

(x^4+6x^2+9)=x^2+3

no

Is the following statement true:

(x^4+6x^2+9)^1/2=x^2+3

yes.

I thought is was no.

When asked this question by someone, I could not get the left side to look like the right.

x^2+ x(6)^1/2+3=x^2 +3

How does this simplify any further?

x^2+ x(6)^1/2+3=x^2 +3

makes no sense at all.
6^(1/2) is not zero

(x^2+3)^2 = x^4 + 6x^2 + 9

so, x^2+3 = √(x^4+6x^2+9)

But,
√(x^4+6x^2+9) = (x^4+6x^2+9)^1/2

so,

(x^4+6x^2+9)^1/2 = x^2+3

I know that, which is why I thought the answer was no, but then I was told that the answer was yes. I couldn't simplify nor reason it any further than what I have submitted. If you can show how to do it, it would be greatly appreciated; the problem is kind of bugging me.

Got it.

I was totally overthinking this.

To determine if the statement is true, we need to compare the left-hand side (LHS) and the right-hand side (RHS) of the equation and check if they are equal.

The LHS of the equation is (x^4 + 6x^2 + 9), while the RHS is (x^2 + 3).

To check their equality, we'll simplify both sides by combining like terms and determining if they are equal.

Starting with the LHS:

(x^4 + 6x^2 + 9)

We see that there are no like terms to combine, so we can't further simplify it.

Next, let's simplify the RHS:

(x^2 + 3)

Since there are no like terms to combine on this side either, it is already in simplified form.

Now, we compare both sides of the equation:

LHS: (x^4 + 6x^2 + 9)
RHS: (x^2 + 3)

By comparing the LHS and RHS, we can see that they are not equal.

Therefore, the statement (x^4 + 6x^2 + 9) = (x^2 + 3) is false.