Let `(x,y)` be a pair of real number satisfying `56x+33y=-(y)/(x^(2)+y^(2))` and `33x-56y=(x)/(x^(2)+y^(2))`. If `x/y=(p)/(q)` (where p and q are relatively prime and `pgtq`) then `(6p-q)` is

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4)and y=2xy is :

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4) and y=2xy is

Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(3) -1) for x gt 1 is (p)/(q), where p and q are relatively prime natural numbers, then p+ q=

If x,y,z are positive reals such that x^(2)-y^(2)+z^(2)=7:xy+yz+zx=4 then the minimum valueof (4-(y+x)z) is (p)/(q) (where p,q are relatively prime).Find the value of (p+q)

If AM and GM of x and y are in the ratio of p:q, then x:y is

If x and y are real then the number of ordered pairs (x,y) such that x+y+(x)/(y)=(1)/(2) and (x+y)(x)/(y)=-(1)/(2) is

If (x+iy)(p+iq)=(x^(2)+y^(2))i, prove that x=q,y=p

Let x and y be the positive real numbers such that log_x y=-(1)/(4) , then value of the expression log_x(xy^5)-log_y""((x^(2))/(sqrt(y))) is (p)/(q) then q is _____________. { where p , q in N and are coprime to each other }

Solve for x and y:(q)/(p)x+(p)/(q)y=p^(2)+q^(2);x+y=2pq

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