If `xsqrt(2) + ysqrt(3) = 0` where x and y are rational numbers, show that `x = y = 0`.

If x, y are rationals and xsqrt(2) - ysqrt(3) = 0 , show that x = y = 0

xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=

If ysqrt(1-x^2)+xsqrt(1-y^2)=1 when |x|lt1 and |y|lt1 find dy/dx

xsqrt(1-y^(2))dx+ysqrt(1+x^(2))dy=0

xsqrt(y^(2)-1)dx-ysqrt(x^(2)-1)dy=0

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

If x^3 + y^3 = 3ax^2 , show that y_2 + (2a^2x^2)/(y^5) = 0

The greatest value x^2y^3 is, where xgt0 and ygt0 are connected by the relation 3x+4y=5

If y = x^(5) show that x(dy)/(dx)-5y = 0 .