Practice problem
Which of the following inequalities are true for all real numbers xxx and y?y?y?
−x2+2xy−y2+4ex2+y2≤2(ex+ey)-x^2 + 2xy - y^2 + 4e^{\frac{x}{2} + \frac{y}{2}} \leq 2(e^x + e^y)−x2+2xy−y2+4e2x+2y≤2(ex+ey)
−x2+2xy−y2+4ex2+y2≥2(ex+ey)-x^2 + 2xy - y^2 + 4e^{\frac{x}{2} + \frac{y}{2}} \geq 2(e^x + e^y)−x2+2xy−y2+4e2x+2y≥2(ex+ey)
(x+y)2+4ex2+y2≤2(x2+ex+y2+ey)(x + y)^2 + 4e^{\frac{x}{2} + \frac{y}{2}} \leq 2(x^2 + e^x + y^2 + e^y)(x+y)2+4e2x+2y≤2(x2+ex+y2+ey)
(x+y)2+4ex2+y2≥2(x2+ex+y2+ey)(x + y)^2 + 4e^{\frac{x}{2} + \frac{y}{2}} \geq 2(x^2 + e^x + y^2 + e^y)(x+y)2+4e2x+2y≥2(x2+ex+y2+ey)
(x+y)2+2ex2+y2≤2(x2+ex+y2+ey)(x + y)^2 + 2e^{\frac{x}{2} + \frac{y}{2}} \leq 2(x^2 + e^x + y^2 + e^y)(x+y)2+2e2x+2y≤2(x2+ex+y2+ey)
(x+y)2+2ex2+y2≥2(x2+ex+y2+ey)(x + y)^2 + 2e^{\frac{x}{2} + \frac{y}{2}} \geq 2(x^2 + e^x + y^2 + e^y)(x+y)2+2e2x+2y≥2(x2+ex+y2+ey)
Type a concept, like “slope” or “photosynthesis”.
