Question

Please answer the following
#9

Answer 1

Let x be added to l and M

(l+x)/(m+x) = a²/b²
⇒b²l +b²x = ma²+xa²
⇒x(a²-b²) =( b²l - a²m)
⇒x = ( b²l - a²m)/(a²-b²)

Answer 2

Let we have to add x with both l and m to make their ratio a²:b².
∴, (l+x)/(m+x)=a²/b²
or, lb²+b²x=a²m+a²x
or, x(b²-a²)=a²m-lb²
or, x=(a²m-lb²)/(b²-a²)
or, x=(lb²-a²m)/(a²-b²)
∴, Answer: (2) (lb²-a²m)/(a²-b²)