Question

Determinati cel mai mare nr intreg care verifica inecuatia

x-2√2≥√2x-2

Answer 1

$x- 2\sqrt{2} \geq \sqrt{2}x-2 \Rightarrow x- \sqrt{2}x \geq -2+2\sqrt{2} \Rightarrow \\ \\ x(1-\sqrt{2})\geq -2(1- \sqrt{2}) \Big{|}:(1- \sqrt{2}) \Rightarrow x\leq -2 \\\Big{(} 1- \sqrt{2}\ \textless \ 0 \rightarrow \ daca impartim cu 1-\sqrt{2} se schimba semnul inecuatiei\Big{)}\\ \\ \Rightarrow \ Cel mai mare numar intreg care verifica inecuatia este -2.$