IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

kaymant

Challenge no. 3 for daredevils

rahilarora

hi there i am a student of +2 and a new member it is purely a guess.

ae^x=1+x+x^2/2 ....1
diff wrt x
ae^x=1+x ........2
equating 1& 2
1+x=1+x+x^2/2
=>x^2/2=0
=>x=0

pls give me sol. of this
pls give me some suggestions as i want to drop 1 year for iit prep.

GoNik

i dont think it has jus one real root...newayz will try ....

kaymant

you already can see that x=0 is not a root of given equation by putting x=0 in it except when a = 1(which is not given)

hsbhatt

to see if a root exists check whether there is a sign change between $x \rightarrow -\infty$ and $x \rightarrow \infty$

animal

as we can see that this function is continous as well as diffrentiable foor all real no so applying rolles theorem we get that ther ther is only one root of the eqn

the thing on the rhs will be become zero sometime if we go on diffrentiating but the thing on lhs will not become zero unless a=0 which is not possible .

so it has only one root

hope u got it.............

kaymant

waited for long... posting the solution.

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