If x and y are positive quantities whose sum is 4 , show that `(x+1/x)^(2)+(y+1/y)^(2)ge 12 1/2 `

If x+y+z=1a n dx ,y ,z are positive, then show that (x+1/x)^2+(y+1/y)^2+(z+1/z)^2>(100)/3

If a, b, x, y are positive natural numbers such that (1)/(x) + (1)/(y) = 1 then prove that (a^(x))/(x) + (b^(y))/(y) ge ab .

If z=x+iy and |z-1|+|z+1|=4 show that 3x^(2)+4y^(2)=12

For all positive values of x and y, the value of ((1+x+x^(2))(1+y+y^(2)))/(xy) ,is

The equation of the straight line passing through the point (4,3) and making intercepts on the co-ordinate axes whose sum is -1 is (a) (x)/(2)-(y)/(3)=1 and (x)/(-2)+(y)/(1)=1(x)/(2)-(y)/(3)=-1 and (x)/(-2)+(y)/(1)=-1 (c) (x)/(2)+(y)/(3)=1 and (x)/(2)+(y)/(1)=-1(x)/(2)+(y)/(1)=-1 and (x)/(-2)+(y)/(1)=-1

If x=sin((1)/(a)log y), show that (1-x^(2))y_(2)-xy_(1)-a^(2)y=0

If x=sin((1)/(a)log y), show that (1-x^(2))y_(2)-xy_(1)-a^(2)y=0

If log y=tan^(-1)x, show that (1+x^(2))y_(2)+(2x-1)y_(1)=0

If x+y=a and x+2y=2a are the adjacent sides of a rhombus whose diagonals intersect at (1,2), then sum of all possible values of a is

If 2^(x)=3^(y)=12^(z) show that (1)/(z)=(1)/(y)+(2)/(x)