Show that the equation 2^x = 2 − x^2 has at least two real roots

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Show that the equation 2^x = 2 − x^2 has at least two real roots

Mathematics
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Solve for 0, then factor.
use the determinate..i think its called of the quad formula.... if its 0 only 1 root, if it (+) 2 roots, it its (-) imaginary roots
but its 2^x an exponential fuction...so how to use quadratic here ?

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thought that was a typo lol
its called the discriminant
Same here.
soooo close......
b^2-4ac
but how does discriminant help ?
\[-x^2+2^x -2 = 0\]
x^2 = -2^x +2 square root both sides?
x = +-sqrt(-2^x +2)
sry but i m still in a fix ....jeezzzzz
that doesnt tell you the roots, but it might show that there are 2 of them :)
ahh..got ya !!!
hey but the roots can be complex by taking the roots???
by taking the square root
roots can be complex and most are... but the only one to concern yourself with are the "real" roots
yes...when it was +- sqrt( 2- 2^x). that does not show that v r gonna get two real roots which is the question asking for?
if you wanna limit your self to even values of x
but there is no domain given in the question
meanwhile i checked on wolfram alpha
oh wait... is it (-2)^x or -(2^x)??
they had a graph which cuts on two points
the latter one
maybe log rules would help
would you know guys what is uniform continuity?
log(2^x) = log(2-x^2) x log(2) = log(2-x^2) log(2) = log(2-x^2)^1/x 2 =xroot(2-x^2) ??
uniform?... id have to look it up
ok
f(x) = sin x is continuous on R. Is it uniformly continuous on R?
id vote yes, its periodic, repetitive, and constantly the "same"
if "x" is a fraction that gets us back to integer exponents with the first question....
http://www.wolframalpha.com/input/?i=2^x+%3D+2+%E2%88%92+x^2 check out that one for me plsssssss
..... yeah.....thats correct :)
so u think graph would be enough?
the graph itself is visual proof, the mathematical proof seems a but difficult to reach.
yes...and the second question like you said or is there any better way?
if you graph the sin function, it sounds as if it would fit a "uniform" continuity.
yes...thank you.... can i ask you anything else or i m just pissing u off :(
lol.... you can ask....i might not have an answer tho :)
how to write pi as a symbol on computer?
on any computer? or in here?
any computer
its the ascii code 227 i think, there should also be a character keyboard in your menu that will bring up a virtual keyboard to find it on
yeah mayb in microsoft word ...they might have it ...thanx
programs..accessories....system tools....character maap is where mine is
hey let me check that one ...thanx
П lol
hey u got that...i might copy it n save it on word ...lol
ППППППППППП hhahah
Пп hehehe
lim x->pi/3 ((3+2cosx)^1/2 - 2) / ln (1+sin3x) ??? whats ur views on that one?
pi/3 = 60 degrees..... is [sqrt(3+2cos(x)) - 2] / ln(1+sin(3x)) right?
exactly
sqrt(3+2cos(60)) - 2 sqrt(3 + 2(1/2)) - 2 ------------------- = ----------------- ln(1+sin(180)) ln(1+0)
but thats a limit question ...plugging in the values making it 0/0
sqrt(4) - 2 0 --------- = --- ln(1) 0 I see the dellima
the derivative of each would be....
Dx(ln(x)) = 1/x Dx(ln(1+sin(3x))) = 3cos(3x)/1+sin(3x) the reciprocal of that is what youll need
Dx(sqrt(3+2cos(x))-2) = -sin(x)/sqrt(3+2cos(x))
-sin(x) (1+sin(3x)) ---------------------- sqrt(3+2cos(x)) (3cos(3x)
yes i was also somewhere there
-sqrt(3) sqrt(3) --------- = -------- is what I get 2(3)(-1)(2) 12
i have got 1/4sqrt3
same thing, rationalize your denominator
sqrt(3)/4(3)
got ya !!! u must b a teacher for sure ... aren't u ?
lol ..... nope, just an unemployed carpenter
wtf??? impossible ...to me u r a GREAT TEACHER !!!! and more of a great human being
thanx :)
u have been so helpful...these questions were all for my next week homwork assignment...now i m so relaxed...thanx bro....really appreciate ur help
Refer to the attachment.

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