For $t0$, prove$$ t+\frac4t\geq4. $$ State when equality holds. For $0

Question

For $t>0$, prove$$ t+\frac4t\geq4. $$ State when equality holds. For $00$, prove $$ \frac ab<\frac{a+c}{b+c}<1. $$

Accepted Answer

(a) Difference $\frac{(t-2)^2}{t}\geq0$, equality $t=2$; (b) Both strict comparisons hold.

Linear Equations and Inequalities