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1. The problem statement, all variables and given/known data

Show that [tex] x^2 = xsinx + cosx [/tex] is true only for two values of [tex] x \in {R} [/tex]

2. Relevant equations

Intermediate value theorem

Mean value theorem (?)

3. The attempt at a solution

I already know how to prove that there is al least one [tex] x \in [1,1.5] [/tex] and another [tex] x \in [-1.5,-1] [/tex] where the equation holds. The thing is that I'm not completely sure how to pove that they are unique, I have a geometric argument buy i feel it can be done using the mean value theorem.

Just for you to know, what i did to find out where the x's are, i took [tex] f(x) = x^2-xsinx-cosx [/tex] and gave values to the function it turns out that [tex] f(1) < 0 [/tex] and [tex] f(1.5) > 0 [/tex] so there must be at leat one [tex] x \in [1,1.5] [/tex] where [tex] f(x) = 0 [/tex] But that's it, I ran out of ideas although i feel I'm really close.

Any ideas or advices will be appreiciated

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# Homework Help: Mean value theroem?

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