Nice use of some algebraic identities. Personally, I think it would be more straightforward to solve by guessing the x=-2 solution and then algebraic long division (or comparing coefficients method).
@@GoatedGamer-v7n x^2 - x^3 = 12 => this is given x^3 - x^2 + 12 = 0 => you move x^2 - x^3 from the left of the equation to the right to get 0 = 12 - x^2 + x^3 you rewrite it as 0 = x^3 - x^2 + 12 then x^3 - x^2 + 12 = 0
Most of these questions only want integer solutions. x^2 - x^3 = 12 x^2 * (1 - x) = x * x * (1 - x) = 2 * 2 * 3 but also -2 * -2 * 3 by comparison of terms x = -2
I solved that in like 15 seconds. I started at going through possible numbers and started at 2 since 1-1=0, I knew 2^2=4 and 2^3=8 which add to 12. I knew I was on the right track. So i used -2 as x and it worked
Too much effort used to get rid of the minus-sign in the denominator! Why not solve x^2 -3x = -6 instead? Or, by completing the square, (x-3/2)^2 = 9/4 -6 =−15/4
it was really a good video. it was intuitive and simple
I am grateful you enjoyed it
Nice use of some algebraic identities. Personally, I think it would be more straightforward to solve by guessing the x=-2 solution and then algebraic long division (or comparing coefficients method).
That's the beauty of mathematics. You can use different approaches and still arrive at the same answer.
Or, having found x = -2, divide the original equation by 2 using synthetic division: 2| -1 +1 +0 -12|
x^2 - x^3 = 12
x^3 - x^2 + 12 = 0
(x + 2)(x^2 - 3x + 6) = 0
x = -2, (3 +/- i✓15)/2
Wouldn't it be -12 in the beginning instead of +
@@GoatedGamer-v7n
x^2 - x^3 = 12 => this is given
x^3 - x^2 + 12 = 0 => you move x^2 - x^3 from the left of the equation to the right to get 0 = 12 - x^2 + x^3
you rewrite it as 0 = x^3 - x^2 + 12
then x^3 - x^2 + 12 = 0
@@cyruschang1904 didn't notice u switched x^3 and x^2
@@GoatedGamer-v7n 🙂
Excellent. I would have used remainder and factor theorem
Well explained
Thanks, brother. I'm glad you enjoyed it.
Most of these questions only want integer solutions.
x^2 - x^3 = 12
x^2 * (1 - x) = x * x * (1 - x) = 2 * 2 * 3 but also -2 * -2 * 3
by comparison of terms x = -2
Yea, you're right.
But the question did not indicate that x is a real number. That is why the other values of x are also considered.
Divide by x+2 and we get also x^2-3x+6=0 (besides x+2=0)
This is a good video , easily understandable and simple . Keep the good work
Thanks, I appreciate it.
I solved that in like 15 seconds. I started at going through possible numbers and started at 2 since 1-1=0, I knew 2^2=4 and 2^3=8 which add to 12. I knew I was on the right track. So i used -2 as x and it worked
Yehhhhhhh
umm i just guessed x.=-2
Easy using ruffin rulles
Why won’t you use quadratic formula from the start?
This question is not quadratic. It is a 3rd degree polynomial.
@@SpencersAcademy my bad)
-2
X = -2 in only 10 seconds
Thats -2
couldnt we have made out the answer from x^2 + x^3 = 2^2 + 2^3
… it said x^2 - x^3
No because it was x^2 - x^3
@@jeddy2925 just assume x is negative and the equation turns into x^2 + x^3 which are just the divisors
@@BlingBlong-d1o assume x is negative then you can rewrite it as x^2 + x^3
Too much effort used to get rid of the minus-sign in the denominator! Why not solve x^2 -3x = -6 instead? Or, by completing the square,
(x-3/2)^2 = 9/4 -6 =−15/4
It is -2
Seems more like an IQ test. -2
Yeah. When you just focused on the real values.
Sir, the letters very small and unable to identify easily. Please make them larger.
-2
Yeah, you're right