it was a simple sum but its aftermath wa too much
d/dx of under root 1-cos2x/1=cos2x (means whole function under root)
easily solved it to tan^x now under root means tan x so answer sec^2 x simple
but not the right answer answer was sec^2x if tanx>0 and -sec^22x if tan x<0
started reseaching over it and my borther told me it was some problem of square roots
after that
i confused on even this one
x^2=25 find value of x
so what do we do we root both sides of the equation
so x=root 25 but root 25 is always =5 not -5 ........
but we always write x=+5,-5
i dont know whats right now pls help..
1x2=25 is a quadratic equation(of the 2nd degree) as the highest power of x is 2.
For any equation of nth degree,there are n roots. So here there have to be 2 values of x satisfying this equation.
x2=25
=> x2-25=0
=>(x+5)(x-5)=0
therefore x=5 or x=-5.
23see its simple
just remember always that : root of a number is always positive
so if someone asks you wat is √25
then the ans is only 5 .
nw suppose someone asks u x2=25
wat are possible values of x ??
now der are 2 ways . one is how arka has done.
another is
x2 = 25
so x = + √25
= + 5
hence x = 5 or - 5
remember these steps . I m writing it plus minus bcz , writing √25 only with a plus sign will give me only 5 , since , as i hav already quoted above , √25 is only 5 . But we know - 5 is also a root , hence plus minus .
eg:(1)√x2 = x
eg:(2) x2 = y
then x = + √y
If u hav studied system of equations , then u can use dat too
see x2 =25
is an eqn of degree 2 . Hence it shud hav 2 roots , viz 5 , -5
while x=√25 is an eqn of degree 1 , and hence only 1 root , i.e 5
i hope i havent confused u more
23and for that d/dx sum that u mentioned above ,
u got √function = tanx
now we know sq root shud be positive . now if tanx is +ve, the condition is satisfied . But if tanx becomes negative . Hence the condition gets violated. So in order to maintain that condition ,
we make the RHS term position by writing a minus sign .
i.e ifff , tanx < 0
so
- tanx > 0
1kkk i think i got the answer of root of x^2 is always modulus of x
edited
1But guys,there have to be 2 roots of a quadratic-even though they maybe equal in some cases[e.g. (x-2)2=0 both roots are 2.]
and yes √x2=|x|