If x and y are positive real numbers , then prove that `x lt y iff x^2 lt y^2`

Are there numbers x, y such that |x+y|lt|x|+|y| ?

Suppose x and y are real numbers such that -1lt xlt ylt 1 . Let G be the sum of the geometric series whose first term is x and whose common ratio is y, and let G' be the sum of the geometric series whose first term is y and common ratio is x. If G=Gʻ, then the value of (x +y)

Write the negation of the following statements r : For every real number x, either x gt 1 or x lt 1

Which of the relations R on the set of the real numbers is an equivalence relation? (a).x R y if |x|=|y|

Find two positive numbers x and y such that x+y=60 and x y^3 is maximum.

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

The set of all real numbers satisfying the inequality X - 2 lt 1 is

Check whether the following pair of statements are negation of each other Give reasons for your answer. i)x+y=y+x is true for every real number x and y. (ii)There exist a real number x and y for which x+y = y+x.

If x and y be real, show that the equation sec ^(2) theta=(4 xy)/((x+y)^(2)) is possible only when x=y