Number of imaginary roots of (x+1)^1/2+(x-1)^1/2=1,is

(a) 0

(b) 1

(c)2

(d)4

on squaring both sides, we have

x+1+x-1+2(x²-1)^1/2 =1

so, we have

2x + 2(x²-1)^1/2=1

or 1-2x = 2(x²-1)^1/2

on squaring both sides again we have

1+4x² -4x = 4x² -4

so , x = 5/4 so roots are real

no imaginery roots

option is A

Mr. Ramesh,

I have a doubt here,

I solved this q and got x=5/4 as the answer but as my teacher always asks me to substitute the value I got in the given equation and see whether it satisfies or not.

In this case x=5/4 does not satisfy the eqn.

So, there is no real root but 1 imaginary root.