no. of real solution in exp. equation

Total no. of real solution of

My Trail:: Let and

Now Using first derivative test, we will check whose slope is Increasing faster rate.

So and

So for The , Slope of Slope of

So is always above

So no solution for

and for Slope of Slope of

So is always above

So no solution for

Now we will calculate in

Now I Did not understand How can I find whether is or not

please help me

Thanks

1 Attachment(s)

Re: no. of real solution in exp. equation

Never underestimate the power of a picture. It will help you refine your solution.

And you missed an obvious solution: (x, y) = (0, 1).

-Dan

Re: no. of real solution in exp. equation

Thanks moderator

Yes is obivious solution of given equation.

Now my question is how can I check these two graph intersect in or not.

and How can we draw figure of these graph in

Thanks

Re: no. of real solution in exp. equation

Quote:

Originally Posted by

**jacks** Thanks moderator

Yes

is obivious solution of given equation.

Now my question is how can I check these two graph intersect in

or not.

and How can we draw figure of these graph in

Thanks

The graph provided by Topskward is the answer to the last line of your post.

Re: no. of real solution in exp. equation

Do you have to show proof (algebraic) ?

Re: no. of real solution in exp. equation

Quote:

Originally Posted by

**chen09** Do you have to show proof (algebraic) ?

It has to be iterative solution

Re: no. of real solution in exp. equation

Quote:

Originally Posted by

**votan** It has to be iterative solution

I tried Newton-Raphson. It either converges to 1 or it becomes unstable depending on initial guess. I think bisection method should work but I did not put time on it. I found the other root graphically: x = -0.57203.

2^(-0.57203) = 0.6727

1 - x^2 = 0.6728

Re: no. of real solution in exp. equation

Quote:

Originally Posted by

**votan** Topskward

!!!!!!

-Dan

Re: no. of real solution in exp. equation

Quote:

Originally Posted by

**topsquark** !!!!!!

-Dan

I was wandering what is this. I went back to may posts. I am still laughing from it. My apology for mispelling topsquark