Question

Determinati inegalitatea :
√21 - √5 ≥√20 - √5
Explicit!

Answer 1

rad(21)-rad(5)>=rad(20)-rad(5) <=> rad(21)>=rad(20) <=> 21>20 (adevarat).

Answer 2

"√21 - √5 ≥√20 - √5 "

Notez 20 =a și 5 = b, iar inegalitatea devine:

$\it \sqrt{a+1} -\sqrt{b} \ \textgreater \ \sqrt{a} -\sqrt{b}|_{+\sqrt{b}} \Leftrightarrow \sqrt{a+1} \ \textgreater \ \sqrt{a} \ (adevarat\ \forall a \in \mathbb{N})$