IIT JEE , AIEEE Forum - Mathematics , Algebra

nity

Please check out the number of real roots for the equation

x² +x + x - 1 / x³- x =5/2and the number of imaginary roots for the equation

x + 1 + x - 1 = 1. I have got 4 for the first one and 0 for the second but it is not matching with the book.

ankur.kkhurana

a second one doesnot hav a real root

lazycol

Q2:

(x+1) +

(x-1) =1

squaring both sides,2

(x² -1) = 1-2x

again square, 3x² - 4x +2 =0

D < 0 ie no: of real roots= 0; img roots = 2

nity

please check for the first one also. Is it 4??

Oldisgold

Just see whether the following solution is adequate for Problem no 2

Rearranging the terms :

(x + 1) = 1 -

(x-1) , squaring

x + 1 = 1 + (x-1) - 2

(x - 1)

Cancelling and rearranging :

1 = - 2

(x -1 ) : solving

(x-1) = - (1/2) {read as minus (1/2) }

Retain only the minus root of

(x-1).

Solving for X ,w e get

X = (5/4) , but

(x -1 ) = minus (1/2). ie + root is ignored.

This solution set satisfies the problem as given above

(x +1) +

(x-1) = Sqrt of (9/4) - (1/2) = 1. QED.

Is the above satisfacotry ?