Find all solutions for x in 2(2x−1)x2+(2x2−2)x=2x+1−2. Prove your answer
I checked and there are no mistypes. I have changed it to latex so you can look at it easier.
+30 Oh, the LaTeX version is much clearer.
Simply both sides first so you can isolate the variable.
Remember, isolate, isolate, isolate.
x=−1,0,1
x can be -1, 0, or 1.
+118696
2(2x−1)x2+(2x2−2)x=2x+1−22(2x−1)x2+(2x2−2)x=2(2x−1)2(2x−1)x2−2(2x−1)=−(2x2−2)x2(2x−1)(x2−1)=−(2x2−2)x
By inspection,
If both sides equal zero then they both must be the same.
If x=0 both sides are zero so that is a solution.
If x= +1 or -1 they are solutions too.
If x is bigger than 1 then the left side is positive and the right side is negative so no answers there
If x is less than -1 then the left side is negative and the right side is positive so no answer there either.
So could there be any more answers between -1 and +1?
I do not think so but i do not know how to prove it.
Maybe CuriousDude can show us both. 
