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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 July 6th, 2018, 02:11 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 591 Thanks: 87 Inverse Logic From A we solve B or $\displaystyle A\rightarrow B$ By inverse we get $\displaystyle B\rightarrow A \rightarrow A\equiv B$ Let's use it to solve equations below: Given equation $\displaystyle a(x)=b(x)$we transform to $\displaystyle a(x)-b(x)=0$ or $\displaystyle z(t)=0$ From $\displaystyle \frac{dz}{dt} =0$ we find extremum of $\displaystyle z(t)$ (if it exist ofc) Now by inverse theory we find value $\displaystyle t_0$ for which $\displaystyle \int z(t)dt=E[\int z(t)dt]$ so now we have an equivalence $\displaystyle \frac{dz}{dt}=0 \equiv \min\{ \int z(t)dt \}=\int z(t)dt$ Let's take a great example below: Given equation $\displaystyle x=\sin x$ we transform to $\displaystyle x-\sin x =0$ now if value $\displaystyle x_0$ satisfies the equation $\displaystyle \frac{1}{2} x^2 +\cos x = \min( \frac{1}{2} x^2+\cos x )$ then $\displaystyle x_0$ holds for $\displaystyle x_0=\sin x_0$ For those who further info, I have solved equations with this method like below: $\displaystyle e^x=x+1$ , $\displaystyle e^x=ex$ , $\displaystyle a^x=x+1 ...$ etc Last edited by skipjack; July 6th, 2018 at 06:07 AM. July 6th, 2018, 02:36 AM #2 Senior Member   Joined: Oct 2009 Posts: 850 Thanks: 325 Yes, root finding problems and minimization problems are closely related. So what is your point? Tags inverse, logic Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post dmnte Computer Science 0 April 23rd, 2015 10:45 PM KyVanchhay Math Events 1 July 31st, 2013 01:51 AM orokusaki Applied Math 4 April 4th, 2012 05:03 AM jaredbeach Algebra 1 November 17th, 2011 11:58 AM JOANA Abstract Algebra 0 March 18th, 2011 06:29 AM

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