Question

X aparține Mulțimii nr. Naturale

Answer 1

 

$\displaystyle\bf\\a)\\(\sqrt{5}-2)x\leq(\sqrt{20}-4)\\\\x\leq\frac{(\sqrt{20}-4)}{(\sqrt{5}-2)}\\\\\\x\leq\frac{(\sqrt{4\cdot5}-4)}{(\sqrt{5}-2)}\\\\\\x\leq\frac{(2\sqrt{5}-4)}{(\sqrt{5}-2)}\\\\\\x\leq\frac{2(\sqrt{5}-2)}{(\sqrt{5}-2)}\\\\x\leq2\\\\\boxed{x\in\{0;~1;~2\}}\\\\\\b)\\(1-\sqrt{3})x>(5-\sqrt{75})~~~\Big|\cdot(-1)\\\\(\sqrt{3}-1)x<(\sqrt{75}-5)\\\\\\x<\frac{(\sqrt{25\cdot3}-5)}{(\sqrt{3}-1)}\\\\\\x<\frac{5(\sqrt{3}-1)}{(\sqrt{3}-1)}\\\\\\x<5\\\\\boxed{\bf x\in\{0;~1;~2;~3;~4\}}$