If `x=2+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1.` prove that: `1+a b+a^2b^2+oo=(x y)/(x+y-1)`

Options

A. `(xy)/(y+x-1)`
B. `(x+y)/(x-y)`
C. `(x^(2)+y^(2))/(x-y)`
D. None of these

Answer

A

Explanation

Here, `x=(1)/(1-a), y=(1)/(1-b)`
`rArr a=(x-1)/(x)`
`b=(y-1)/(y)`
`therefore 1+ab+a^(2)b^(2)+ …=(1)/(1-ab)`
`=(xy)/(x+y-1)`