If `ax+(b)/(x) ge c`, for all positive values of x, then show that, `4abgec^(2)`, where a,b,c are positive constants.

If ax^2+b/xgec for all positive x where agt0andbgtc show that 27ab^2ge4c^3

prove that E(ax+b)=aE(x)+b where a and b are constants

If three equal positive numbes a,b,c are in G.P,then show that a+c>2b

For all positive values of x, if ax^(2)+(b)/(x) ge c (where a ge 0, b ge0 ), prove that, 27ab^(2) ge 4c^(3) .

Evaluate: lim_(x->oo) (1+1/(a+bx))^(c+dx) , where a,b,c and dare positive

Prove that, f(x) =x+2+(x-2)e^(x) is positive for all positive values of x.

If three unequal positive numbers a, b, c are in G.P. then show that, a +c gt 2b .

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

Show that f(x) = (x-2)e^x + x + 2 is positive for all positive values of x.

If 2 + i and sqrt5-2i are the roots of the equation (x^2+ax+b)(x^2+cx+d)=0 , where a,b,c,d are real constants, then product of all roots of the equation is