Question

If `2*sqrt(3(2/4)*(3/5)*(4/6)...(x/y))=1` then (x,y)=?

Answer 1

`2* sqrt(3(2/4)*(3/5)*(4/6)...(x/y))=1`

By inspection it is obvious that `y=x+2`

`=>2*sqrt(3(2/4)*(3/5)*(4/6)...(x/(x+2)))=1`

`=>2*sqrt(3*(2*3)/((x+1)(x+2)))=1`

Squaring both sides we get

`=>(4*3*2*3)/((x+1)(x+2))=1`

`=>x^2+3x+2-72=0`

`=>x^2+3x-70=0`

`=>x^2+10x-7x-70=0`

`=>x(x+10)-7(x+10)=0`

`=>(x+10)(x-7)=0`

X can't be negative.

Hence `x=7 and y=x+2=9`