`(l)/(m)x^(2)+((l)/(m)+(p)/(q))x+(p)/(q)`

If (p)/(x) +(q)/(y) =m and (q)/(x) +(p)/(y) =n , then what is (x)/(y) equal to ?

Simplify (i) ((x^(i))/(x^(m)))^((1)/(lm)).((x^(m))/(x^(n)))^((1)/(m)).((x^(n))/(x^(l)))^((1)/(nl)) (ii) ((x^(p))/(x^(q)))^((1)/(ml)).((x^(q))/(x^(r)))^((1)/(mn)).((x^(r))/(x^(p)))^(r+q)

{(P+1/(q))^(m).(p-(1)/(q))^(n)}/{(q+(1)/(p))^(m).(q-(1)/(p))^(n)}

Simply (x^(p)/x^(q))^(p+q)div((x^(p+q))/(x^(p-q)))^(p^(2)/(q))

Let A=[(l,m,n),(p,q,r),(1,1,1)] and B=A^(2) . If (l-m)^(2)+(p-q)^(2)=9, (m-n)^(2)+(q-r)^(2)=16, (n-l)^(2)+(r-p)^(2)=25 , then the value of |det(B)-140| is_______

The equation of the line common to the pair of lines (p^(2)-q^(2)) x^(2)+(q^(2)-r^(2)) x y+(r^(2)-p^(2)) y^(2)=0 and (l-m) x^(2)+(m-n) x y+(n-l) y^(2)=0 is

Let det A=|{:(l,m,n),(p,q,r),(1,1,1):}| and if (l-m)^2 + (p-q)^2 =9, (m-n)^2 + (q-r)^2=16, (n-l)^2 +(r-p)^2=25 , then the value ("det." A)^2 equals :

Let det A=|{:(l,m,n),(p,q,r),(1,1,1):}| and if (l-m)^2 + (p-q)^2 =9, (m-n)^2 + (q-r)^2=16, (n-l)^2 +(r-p)^2=25 , then the value ("det." A)^2 equals :