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

1 Answer
P dilip_k
Jul 20, 2018

#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#

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