THe way i see it, it's only negatives that make this equation useless, but my teacher said there are a billion numbers that make this equation not work and it's not negative. Guys... math geniuses, how is this even possible ?! Thanks. --------------------- WOW i NEVER thought THAT many people would reply to this. So far, i've read most of them and I dont want to say anything about anyone, but my teacher told me the answer is - Negatives, and imaginery numbers. X HAS to be an absolute value which some of you said. Most of you said that, so thanks for da help. but in any case, Thanks I never thought ppl would really reply to this thread! (even thou half of the replies were flaming, but w/e! )
I learned this last year, but I forgot what base 10 means. And I'm not taking math this year . Would you mind refreshing my memory? *gives puppy-dog eyes and pouts*
You've failed Algebra II! Good job! John Kerry says you'll be stuck in Iraq, by the way. What is x? Just an (squarerootsign)x^2=y kind of thing?
SORRY, BUT WHAT MATH ARE U IN? HERE IS AN EXAMPLE FOR THE SLOW PEOPLE: the square root of 9 squared is 9 if you do the squared part which would be 81, then that would be a waste of time, seeing as how the square root of 81 is 9. Squared and square root do cancel eachother out...should have learned that in the 6th grade. imaginary numbers is an exception (man i hate those)
hmm...that does not really make sense to me...but If x is in a different number system than the "Real Number System", (like the "Imaginary Number System"), then that might be true, but I see no other way that the square root of x squared is not x...
their called imaginary numbers. for example whats the square root of -9 squared? Well -9^2 = -81 sqr rot of -81 = impossible. So the square root of -9^2 does not exist. Now without the number being negative, Give me a min sqr() = sqare root ^ = exponent Now lets imagine the equation y=x^2+1 Using sqr() as the square root function (as I don't have a square root symbol on the WWW), the equation sqr(x-1)=1-sqr(x+4) seems to have two solutions. Just solve it using traditional algebraic methods. Go ahead and try it. Now, before I tell you about the answer, go ahead and check your work, by substituting your two solutions back into the original equation. It didn't work, did it? This equation has no solution. It seems to have the solutions x=0 and -3. But neither of these works. That is a good reason to check your work. Many equations have no solutions. 2x=2x+3 has no solution. But, when we try to solve that one, we get obvious nonsense, like 0=3. In our more complicated equation, we didn't get obvious nonsense, until we checked our work. What is going on there? Well, our solutions were not imaginary, but imaginary numbers were encountered during the attempted solution, and during the checking of our work. Does that matter? Well yes, in a way. On the left side of our equation we have sqr(x-1), which just may be an imaginary number. On the right side, we have 1-sqr(x+4), which just may be one more than another imaginary number. No imaginary number is one more than any imaginary number. So, where did we go wrong, when we solved it. Well, we probably squared both sides. What if we have the obvious nonsense -2=2? Well, if we square both sides, we get the obvious truth 4=4. So, squaring both sides can be dangerous. We can start with an equation with no solution, square it, and end with an equation with a solution. We are starting with nonsense (maybe well disguised), and ending with something that is not nonsense. Here is an example: x-2=x+2, which has no solution. Square both sides (not something that you would normally do in this case), and you get x²-2x+4=x²+2x+4. Simplify, and you get -2x=2x. Solve for x and you get x=0, which does not work in the original equation (x-2=x+2). That did not involve imaginary numbers. I put it in this article, about imaginary numbers, because similar equations, but with imaginary numbers in them, demand that you square both sides in order to progress toward a possible solution. They encourage you to fall into that trap. I copied that example from a website to save myself time.
Actually, -9^2 is 81, a negative x a negative is a positive. Thus, the square root of x^2 is (plus or minus, the sign isn't on the keyboard or in the symbol thing)+/- x, or |x|, but you are correct, you can't take the square root of a negative number.
Quit using a calculator. What's a negative x negative? Positive. (-9)^2 will give you 81. -9^2 will give you -81. Reason: calculator is only calculating the nine, not the negative attached. Stick parenthesis around it to be safe with negatives.
Yea right, I totally forgot about that :$ Anyways I got an eample from a website to explain it. I haven't done exponents in AGES!
You still need the parenthesis, even if it's on paper. What that states is -(9)^2, which DOES equal -81, whether you want to admit it or not. However, it changes the whole equation to -1*9^2, so it's not a very good example Man, you guys are making me want to get into math again, but I HATE math classes! GRR!
