Question

4. Comparați numerele a= √50+√36-√8+√4 şi b= √125+√64-√45.

Answer 1

$a = \sqrt{50} + \sqrt{36} - \sqrt{8} + \sqrt{4} \\ a = 5 \sqrt{2} + 6 - 2 \sqrt{2} + 2 \\ a = 3 \sqrt{2} + 8 \\ b = \sqrt{125} + \sqrt{64} - \sqrt{45} \\ b = 5 \sqrt{5} + 4 - 3 \sqrt{5} \\ b = 2 \sqrt{5} + 4 \\ \\ presupunem \: \: ca \: \: a < b \\ \implies \: 3 \sqrt{2} < 2 \sqrt{5} \\ (3 \sqrt{2} ) {}^{2} < (2 \sqrt{5} ) {}^{2} \\ 18 < 20 \\\iff \: 18 + 8 < 20 + 4 \\ 26 < 24 \\ \implies \: fals \\ \\ \implies \:\boxed{ a > b}$