x is a real number and `x^(2)+5lt6x` . Then prove that , x must be between 1 to 5 .

Show that if x is real and x^2+5lt6x , then x must lie between 1 and 5.

Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real values of x and y ,then x must lie between 1 and 3 and y must lie between -1/3 and 1/3 .

If 2x^3 + 5x = 0 , where x is a real number, then x = 0’ examine the statement by contrapositive method.

If x and y are real numbers and (x-5)^(2)+(x-y)^(2)=0 , then find the value of x and y.

If ((x-5)(x^2-2x+1))/((x-7)(x^2+2x+3)) is positive for all real values of x, show that x has no value between 5 and 7.

If x is real number, then the minimum value of x^2+x+1 is

Let RR be the set of all real numbers and A={x in RR : 0 lt x lt 1} . Is the mapping f : A to RR defined by f(x) =(2x-1)/(1-|2x-1|) bijective ?

If f(x)=5^x , then prove : f(log_5x)=x

Let agt1 be a real number . If S is the set of real number x that are solutions to the equation a^(2log_2x)=5+4x^(log_2a) , then how many real number S contains?

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4