Question about algebra?

Question

I know when you want to remove division or multiplication in algebra, every term on the left and right side must be either multiplied or divided. For example: 2x + 12 = 20. Normally, people simplify by subtracting 12 from each side, but even if you don't, it still works by doing x + 12/2 = 20/2, which comes out to x + 6 = 10, take away 6 from both sides, and you get 4. However, this doesn't seem to work with squares or square-roots. For example: x^2 + 4 = 20. x + sqrt(4) = sqrt(20) doesn't work. If you simplify beforehand and do x^2 = 16, you get the right answer (4). Why doesn't my first example work? Is there some sort of special rule?

Answer 1

In Algebra, simplifying is very relevant. In your given example, x^2 + 4 = 20, 4 must be transposed first. It is in the rule that you need to transpose all value that has no variables such as x to the other side of the equation. if you do not do this, you might not get the right answer. Your first example happens to have two possible solutions. The second solution, (the one without transposition) is not applicable to the 2nd example. This is under the kinds of equation. The first example is a linear equation. Your second example consists of an exponent that needs to be simplified first. Not all of the equations with or without exponent have the same solutions. There are set of rules needed to be followed in order to achieve the right answer. Hope I helped you! =p

Answer 2

Yes. Square roots and powers do not share the distributive property with multiplication. So, if you take the square root of one side, you have to take the square root of the entire other side.

Ex.
x^2 + 4 = 20
sqrt(x^2 + 4) = sqrt(20)

Now, we've done the same thing to both sides of the equation. Exponents work the same way.

(x^2 + 4) ^ 2 = 20 ^ 2

Answer 3

For example: x^2 + 4 = 20. /= x + sqrt(4) = sqrt(20)
You would need to take the sqrt of (x^2 +4) = sqrt(20), not sqrt x^2 + sqrt of 4.
As if you did sqrt of 4 + sqrt 16 = 6
as opposed to sqrt of (4 + 16) = sqrt of 20 /= 6

Answer 4

.

In first example you divided each term in the equation by same number.

2x + 12 = 20

divide by 2 means

(2x + 12)/2 = 20/2 , this is equal to

2x/2 + 12/2 = 20/2

because
(a + b)/c = a/c + b/c

where as sqrt(a + b) is not equal to sqrt(a) + sqrt(b)

if we apply the operation to the total left side and right side, it is okay

sqrt of (LHS) = sqrt(RHS)


ex

x^2 + y^2 = a^2

then sqrt(x^2 + y^2) = sqrt(a^2) is perfectly alright

Answer 5

If you choose to take the square root of the problem before subtracting, you have to take the square root of (x^2+4) not the square root of x^2 plus the square root of 4. The square root of x^2+4 is an imaginary number, so until you get to the point where you have to deal with imaginary numbers, I would stick with subtracting first.

Answer 6

You attempted to do something that many math students do incorrectly.

You assumed that sqrt(x^2+4) = sqrt(x^2) + sqrt(4)

This is NEVER true.

In fact, there is no real square root of x^2 + 4, making it impossible to solve using that method.

Answer 7

it is supposed to be worked out like this:

(x+2)(x-2)=20

Answer 8

You are assuming that sqrt (a + b) = sqrt(a) + sqrt(b). It
doesn't.

It is true that sqrt(a * b) = sqrt(a) * sqrt(b)

So the rule is that sqrt (a + b) != sqrt(a) + sqrt(b)