For positive numbers $u,v$, use $(u-v)^2\geq0$ to prove $$ u^2+v^2\geq2uv. $$ State when equalit

Question

For positive numbers $u,v$, use $(u-v)^2\geq0$ to prove $$ u^2+v^2\geq2uv. $$ State when equality holds. For $0<a<b$, prove $$ \frac ab<\frac{a+2}{b+2}. $$

Accepted Answer

(a) Difference $=(u-v)^2\geq0$, equality $u=v$; (b) difference $=\frac{2(b-a)}{b(b+2)}>0$.

Linear Equations and Inequalities

Linear Equations and Inequalities

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