Prove that x^2+xy+y^2≥0 for all real numbers, x and y. Find the values that result in equality.
Prove that x^2+xy+y^2≥0 for all real numbers, x and y. Find the values that result in...
If x and y are real numbers and if xy=0, then either x=0 or y=0 Give two examples of a typical problem or calculation in high school algebra in which this role of 0 is used
For all real numbers x and y, if x is not equal to y, x>0,y>0 then (x/y)+(y/x)>2
9. Let x,y > 0 be real numbers and q, r E Q. Prove the following: (а) 29 > 0. 2"а" and (29)" (b) x7+r (с) г а — 1/29. 0, then x> y if and only if r4 > y (d) If q (e) For 1, r4 > x" if and only if q > r. For x < 1, x4 > x* if and only if q < r.
Prove that for any two real numbers x and y, |x + y| ≤ |x| + |y|. Hint: Use the previously proven facts that for any real number a, |a|≥ a and |a|≥−a. You should need only two cases.
Show that if x and y are real numbers, x2 + y2 >= 2xy and (x + y)2 >= 4xy; When does equality hold (with proof)? Show that if x and y are real numbers, x2 + y2 2xy and (x y) 2Hry. When does equality hold (with proof)?
Prove that for positive real numbers x and y, the following inequality holds:
Consider the solution to the IVP y' - xy = x; y(0) = 2 Find y' (0) Consider the solution to the IVP y' - xy = t; y(0) = 2 Find y" (0)
Suppose R is the relation defined on all real numbers by for all real numbers x,y (xRy if |x-yl3) Then for real numbers x and y, xR2y iff
Find values of x and y such that both fx(x,y) = 0 and fy(x,y) = 0. f(x,y) = x² + xy + y2 - 3x +2 A. X=2, y= -1 OB. X = -2, y=1 O c. 1 x= 1, y = 2 OD. x= 0, y = 0
Find the general solution around x=0 for (x^2-x)y’’-xy’+y=0