Math problems ! :D

[15357]

Was bored, so posted the problems that I learned (and have some problems with) :E
If you figure it out, i'l send you a cookie.

#1)
If x^2 - 2x - 1 = 0, x = a OR b. and if x^2 - x + 2 = 0, x = c OR d,
What is P in this equation? P = (c-a)(c-b)(d-a)(d-b)

 

[ktimekiller]

Aw shit, i knew i should have stayed in korea, im in 9th grade to be still learning algebra =/

 

[Cormeh]

Seen as I'm no mathematician, I'd first ask what the value of d could be expressed as. :O

 

[Ikerous]

Am I supposed to be using imaginary numbers? :|

 

[Dan]

Everyone probably knows how to solve quadratic equations. So the first two equations yield:

a = sqrt2 + 1
b = sqrt2 - 1
c = 0.5 + i*sqrt(7/4)
d = 0.5 - i*sqrt(7/4)

(I'm assuming that by b in the second equation you really meant to say d)

P = (c-a)(c-b)(d-a)(d-b)
P = [-0.5 - sqrt 2 + i*sqrt(7/4)]*[1.5 - sqrt2 + i*sqrt(7/4)]*[-0.5 - sqrt 2 - i*sqrt(7/4)]*[1.5 - sqrt 2 - i*sqrt(7/4)]

You can cancel out the imaginary numbers by multiplying the 1st and 3rd term and the 2nd and 4th term because they are both pairs of complex conjugates. After that it's just a matter of simplifying.

P = [(-0.5 - sqrt2)^2 + 7/4]*[(1.5 - sqrt2)^2 + 7/4]
P = [0.25 + sqrt2 + 2 + 7/4]*[2.25 -3*sqrt2 + 2 +7/4]
P = [4 + sqrt2]*[6 - 3*sqrt2]
P = 24 - 6*sqrt2 - 6
P = 6*(3 - sqrt2)
P = 9.514

The equations look kind of long and messy because I didn't simplify any fractions or square roots until the very end. I didn't check any of the math so I might have made a little mistake somewhere, but it's a good solution method atleast.

 

[Dan]

dbl post

 

[15357]

****. I wrote the damned problem inccorectley. x^2 - x + 2 = 0, x = c OR d. But, p = 18.

sorry about that.

#2
The 2 graphs y= 2x^2 -3x + 2, y = ax^2 + bx + 8 has a point in which they coincide.
If the graph y = -x + 6 goes through that coinciding point, what is a and b?

 

[TheSomeone]

P = (c-a)(c-b)(d-a)(d-b)

 

[dfc05]

I got a = -1 and b = 0. But that's probably wrong seeing as the line intersects the given parabola at two points (-1,7) and (2,4), and if a=-1, b=0, that gives a parabola that intersects the first parabola at both those points instead of a single coinciding point. :O

 

[Dan]

care to show the work for the 1st one. I don't get 18.

And the second question has an infinite range of answers. I think you might have written it wrong also. a= 0 b=1 works, a=1, b=2 works, so does a=500, b=501. (a + 1 = b) BTW, all those curves will intersect at (-1,7) which also intersects y = -x + 6. The same could be done for the other intersection point (2,4) yielding the other set of answers (2a + b = -4).

If what you meant to say is that there are two intersection points and y = -x + 6 goes through both of them, then a = -5/3 and b = -2/3

 

[Uriel]

*points to his butt
Thats what i think of Math

 

[15357]

I got a = -1 and b = 0. But that's probably wrong seeing as the line intersects the given parabola at two points (-1,7) and (2,4), and if a=-1, b=0, that gives a parabola that intersects the first parabola at both those points instead of a single coinciding point. :O

Thats actually correct. you cookie will arive in about 217 years, 11 months, 25 days.

and Dan:

x^2+2x-1 = 0 .... x = a OR b
a + b = -2 (because -(2/1) = a+b)
a * b = -1 (because -1/1 = a*b)

x^2 - x + 2 = 0, x = c OR d
c + d = 1
c * d = 2
...
(1)...c^2 - c + 2 =0
...d^2 - d +2 =0

p = {c^2 - (a+b)*c + ab} * {d^2 - (a+b) * d +ab}
.. = (c^2 + 2c -1) * (d^2 + 2d -1) .... (2)

due to (1), (2) = 3(c-1) * 3(d-1) = 9(c*d - (c+d) + 1) = 18

 

[Dan]

and Dan:

x^2+2x-1 = 0 .... x = a OR b
a + b = -2 (because -(2/1) = a+b)
a * b = -1 (because -1/1 = a*b)

x^2 - x + 2 = 0, x = c OR d
c + d = 1
c * d = 2

I don't see how you get to those statements. You changed the equation from the original question. It used to be x^2 - 2x -1 = 0


If x^2 - 2x -1 = 0
then x = 2.414 OR x = 0.414
x = (1 +/- sqrt2)
those don't fit into the equations you just wrote

Also if x^2 - x +2 = 0
then x = 0.5 +/- sqrt(7/4)i
i is the imaginary number such that i^2 = -1

 

[Lou]

Was bored, so posted the problems that I learned (and have some problems with) :E
If you figure it out, i'l send you a cookie.

#1)
If x^2 - 2x - 1 = 0, x = a OR b. and if x^2 - x + 2 = 0, x = c OR d,
What is P in this equation? P = (c-a)(c-b)(d-a)(d-b)

Your math problems suck. Either state them correctly the first time or don't post them at all.

 

[Ikerous]

Seriously XD

Do you have any idea how long i spent doing those problems before i gave up?

Type em right ><

 

[15357]

Alright, sorry people.

I don't know why I keep typing inccorectly.

 

[Dan]

I went back and double checked that my solution was correct for the original problem

 

[15357]

I'm sorry.