help please

[z51]

If x ,y are positive integers, such that ln(x+y)=lnx +lny ,then the value of the expression x^2 + y^2 is equal to:
Α. 169 Β. 100 c. 25 d. 16 Ε. 8

I started using ln laws:
x+y=xy
i applied both sides with squares and got here:
x^2 +y^2 =xy(xy-2)
and now im stuck!
please help

 

[skeeter]

[MATH]xy = x+y[/MATH]
[MATH](xy)^2= x^2+2xy+y^2[/MATH]
[MATH](xy)^2 -2xy = xy(xy-2) = x^2+y^2[/MATH]
from the available choices, [MATH]xy=4 \implies x^2+y^2 = 8[/MATH]

 

[z51]

[MATH]xy = x+y[/MATH]
[MATH](xy)^2= x^2+2xy+y^2[/MATH]
[MATH](xy)^2 -2xy = xy(xy-2) = x^2+y^2[/MATH]
from the available choices, [MATH]xy=4 \implies x^2+y^2 = 8[/MATH]

how do we know that xy=4?

 

[Deleted member 4993]

how do we know that xy=4?

Response #2 says:

From available choices .......

So try the given numbers and ..,.

 

[skeeter]

how do we know that xy=4?

[MATH]xy(xy-2) = x^2+y^2[/MATH] is not a perfect square ... note choices A, B, C, and D are all perfect square values. Choice E, 8, is not.