If x be real and `0 < b < c` show that `(x^2-b c)/(2x-b-c)` can not lie between b and c.

IF x is real and 0ltmlt1 , show that the expression (x^2+2x+m)/(x^2+4x+3m) is capable of assuming all real values.

If x be real then 2x^(2)+5x-3>0 if

If x , y are real and x + iy=0 then

Let f be a real valued function such that f(x)+3xf(1/x)=2(x+1) for all real x > 0. The value of f(5) is

Let f be a real valued function such that f(x)+3xf(1/x)=2(x+1) for all real x > 0. The value of f(5) is

Write the contrapositive of the following statements: If x is real number such that 0 lt x lt 1 , then x^(2) lt 1 .

For the given statement identify the necessary and sufficent conditions r : If x is real number such that xgt0 " then " x+1/xge2

Given that f(x)gtg(x) for all real x, and f(0)=g(0). Then f(x)ltg(x) for all x belong to

Suppose f is such that f(-x)=-f(x) for every real x and int_(0)^(1)f(x)dx=5, then int_(-1)^(0)f(t)dt=