If `2x^2-3x y-2y^2=7,` then prove that there will be only two integral pairs `(x ,y)` satisfying the above relation.

Find the number of positive integral solutions satisfying the equation (x_1+x_2+x_3)(y_1+y_2)=77.

x+7y=10,3x-2y=7

Find the number of point (x ,y) having integral coordinates satisfying the condition x^2+y^2<25

If x^2 + y^2 = 6xy , prove that 2 log (x + y) = logx + logy + 3 log 2

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

3x-4y=-7,5x-2y=0

If x^2+y^2=x^2y^2 then find the range of (5x+12 y+7x y)/(x y) .

For 0ltx ,yltpi, the number of ordered pairs (x, y) satisfying system equations cot^2(x-y)-(1+sqrt(3))cot(x-y)+sqrt(3)="0 and cosy="(sqrt(3))/2 is

Find the area bounded by the lines y = 2x + 1 and y = 3x + 1 , x = 4 using integration.

If f(2x+3y, 2x-7y)=20x, then f(x,y) equals :