Show that the square roots of two successive natural numbers greater than `N^2` differ by less than `1/(2N)dot`

The roots alpha and beta of a quadratic equation are the square of two consecutive natural numbers. The geometric mean of the two roots is 1 greater than the difference of the roots. If alpha and beta lies between the roots of x^2-cx+ 1 = 0 then find the minimum integral value of c.

Which of the following is not a negative of ''A nature number is greater than zero''

Show that the difference of any two sides of a triangle is less than the third side.

Show that i is neither 0, nor greater than 0, nor less than 0

A number is as much greater than 36 as is less than 86. Find the number.

Write the following statements in symbols and represent them on the number line . Also list the elements of the sets . (i) Whole numbers less than 4. (ii) integers greater than -3 and less than 2.

In a single throw of a die, find the probability of getting a number : (i) greater than 2 (ii) less than or equal to 2 (iii) not greater than 2.

Show that mean and variance of first n natural numbers is (n+1)/(2) and (n^(2) - 1)/(12)

If A is the set of even natural numbers less than 8 and B in the set prime numbers less than 7, then the number of relations from A to B is

If S_1, S_2, S_3 are the sums of first n natural numbers, their squares and cubes respectively, show that 9S_2^ 2=S_3(1+8S_1)dot