Question

The equation has ------ roots?

Answer 1

\[\sqrt{x + 3 - 4\sqrt{x-1}} + \sqrt{x + 8 - 6\sqrt{x-1}}\]

Answer 2

It's not an equation. Do you mean \[\sqrt{x + 3 - 4\sqrt{x-1}} + \sqrt{x + 8 - 6\sqrt{x-1}} = 0\]?

Answer 3

Yes

Answer 4

sorry = 1

Answer 5

no roots..

Answer 6

i can give you a head start for this:
let x-1=y^2
1st term:
\[\sqrt{(x-1)+4-4*\sqrt{x-1}}\]
\[\sqrt{y^{2}-4y+4}\]
\[\sqrt{(y-2)^{2}}\]
+ or - {sqrt(x-1)-2 }
this simplifies 1st term,do it for 2nd term also,equate it to one,lets see whether u get ,x=10,5 as roots,which i got till now
i think there will be 2 more roots,yet to find those,if any

Answer 7

how no roots, doesn't 10 and 5 satisfy the equation,put the values and see...

Answer 8

ohh yes you;re right!!
even now i realize my approach was wrong!!

Answer 9

sorry.....My book says infinitetly many soln

Answer 10

thxxxx