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?
2007-09-19 19:30:18 · 5 answers · asked by Anonymous in Consumer Electronics ➔ Home Theater
Yeah, your brain is knotted. How did you pick this forum to post, by flipping a coin? This is the home theater ELECTRONICS forum, where the discussion is centered around home theater operational and electronics questions.
You want the "Science & Mathmatics-Mathamatics" forum - duh!
2007-09-20 01:40:20 · answer #1 · answered by AWolf 7 · 0⤊ 3⤋
Because the operation you perform must be the same SINGLE operation on both sides of the equation. In the first example, you divided the left side by 2 and you divided the right side by 2. (2x+12)/2 = (20)/2. It's just a nice convenience that (2x+12)/2 = (2x)/2 + 12/2 = x + 6.
The same process on the second equation means you take the square root of the right side and square root of the left:
if x² + 4 = 20, then sqrt(x²+4) = sqrt(20).
Unfortuately, in this case, the distributive property does not work out: sqrt(x²+4) does NOT equal x + 2. However, you CAN do the subtraction first:
x² + 4 - 4 = 20 - 4 (same operation (subtract 4) on both sides)
x² = 16
sqrt(x²) = sqrt(16) (same operation on both sides)
x = 4
2007-09-20 03:51:53 · answer #2 · answered by dansinger61 6 · 0⤊ 3⤋
It is because in general sqrt(a + b) does not equal sqrt(a) + sqrt(b). So you cannot take sqrt of both sides of an equation if sums or differences are involved.
2007-09-19 20:04:09 · answer #3 · answered by gp4rts 7 · 1⤊ 2⤋
yea i think so there might i dont realy know cause i just started learning algebra cheak on a search engine and u might be able to find it.
2007-09-19 19:39:00 · answer #4 · answered by ciarrin kershaw 2 · 0⤊ 3⤋
Can you please give the eqaution better.
2007-09-19 20:05:06 · answer #5 · answered by Pedro Q 3 · 0⤊ 2⤋