Show that the equation x^3 + x^2 -2x = 1 has at least one solution in the interval [-1,1].

Question

asapbleh · Answer

This is how I did it. But i wonder if it is correct.

x^3+x^2-2x=1
x^3-x^2-2x-1=0

x(x^2+x-2-1/x = 0

anonymous · Answer

Plug in both -1 and 1 for x.  If you get one positive and one negative value then the intermediate value theorem states there has to be a value that is 0 somewhere between the two

asapbleh · Answer

Oic, let me try plugging in.

asapbleh · Answer

I dont get it.

anonymous · Answer

was there a y or an f(x) anywhere in the original problem

asapbleh · Answer

No, the whole question was what I stated in the question,

anonymous · Answer

Oh then you have to set the expression to 0 and replace 0 with y to get a function.  Then plug in -1 and 1 for x and if the values for y are positive and negative tthen the intermediate value theorem proves it.  So just take x^3+x^2-2x-1 and plug in -1 and 1

asapbleh · Answer

Oh, ok. lemme try that.

asapbleh · Answer

I got -1=0 and 2=0

anonymous · Answer

but the 0 is a y now so its -1=y and 2=y

anonymous · Answer

|dw:1379297336715:dw| basically you get this and your function goes between these two points (-1,2) and (1,-1) so it has to pass through the x axis somwhere between -1 and 1

asapbleh · Answer

Oh, Ic ic, Thanks, I get it now.