262i am getting 3 solns if a≥e/2 and 1 soln if a<e/2
\hspace{-16}$The no. of solution of the equation $\mathbf{ae^x=1+x+\frac{x^2}{2}}$\\\\ Where $a>0$
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3 Answers
71Say , 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!
71Drawing graph shows something else. I tried from a = e to a = 200e and beyond. There is a solution!
