no. of solution

\hspace{-16}$The no. of solution of the equation $\mathbf{ae^x=1+x+\frac{x^2}{2}}$\\\\ Where $a>0$

3 Answers

71
Vivek @ Born this Way ·

Say , If I write RHS as

ex - ( x3/3!+x4/4! + ..... ∞ )

The expression becomes

( x3/3!+x4/4! + ..... ∞ ) = ex-a ex = ex (a-1)

One Obvious Solution is x = 0 at a =1

However, There are many more solutions for different values of a. Isn't?

Someone verify!

262
Aditya Bhutra ·

i am getting 3 solns if a≥e/2 and 1 soln if a<e/2

71
Vivek @ Born this Way ·

Drawing graph shows something else. I tried from a = e to a = 200e and beyond. There is a solution!

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