IIT JEE , AIEEE Forum - Mathematics , Algebra - find total no. of real solutions of x^2 - 4

umang

[x] means greatest integer function

computer001

no soln...
atleast thts the ans 4 wat uve given...pls chk quest once

umang

the answer given is 2
and the question is correct.
i also think no solution, so just posted to discuss with u all !

ganesha1991

EDIT

elastiboysai

2 solutions exist
clearly from the graph

LAMPARD

See,
x²-4-x+{x}=0 where {x} is frac. part of x.
Thus,it follows that 0<-x²+4+x<1
So,you get x²-x-4<0           and     x²-x-3>0
              (x-1/2)²<17/4       and     (x-1/2)²>13/4
Thus,      x<(

17+1)/2 x>(1+

13)/2
or and or
x>(1-

17)/2 x<(1-

13)2
Thus,     x<2.56                               x<-1.303
                or                    and             or
              x>-1.56                            x>2.3
Thus x has interval (-1.56,-1.303)U(2.3,2.56)
But i am not able to find the 2 solutions to it...

elastiboysai

draw the graph of y=x^2
and y=4+[x]
they intersect at 2 points
so 2 real solutions

elastiboysai

Lampard the question just asks for the no. of real solutions, so no need to find them actually

LAMPARD

Yes,i agree that only no. of solns are asked.Drawing the graph seems to be the best method but then how to find no. of solutions from the intervals calculated???

computer001

im sorry made a mistake :
x^2=4 + [x]
i immediately took x as an integer forgetting tht if x^2 is integer x need not be...sorry 4 error..n thnks elasti

umang

yes got it !
thanks !!!

elastiboysai

heres a graph i plotted wid a software.

Ask & Discuss Questions with Community & Experts