a) \(A = x^{2} - 2 x + 3\) khi \(\mid x \mid = 0 , 5\).

Ta có \(\mid x \mid = 0 , 5\) thì \(x = 0 , 5\) hoặc \(x = - 0 , 5\).

+ Với \(x = 0 , 5\) ta có \(A = 0 , 5^{2} - 2.0 , 5 + 3 = 2 , 25\).

+ Với \(x = - 0 , 5\) ta có \(A = \left(\right. - 0 , 5 \left.\right)^{2} - 2. \left(\right. - 0 , 5 \left.\right) + 3 = 4 , 25\).

b) \(B = x - 3 + \mid 1 - 3 x \mid\) khi \(\mid x \mid = \frac{1}{3}\).

Ta có \(\mid x \mid = \frac{1}{3}\) thì \(x = \frac{1}{3}\) hoặc \(x = - \frac{1}{3}\).

+ Với \(x = \frac{1}{3}\) ta có \(B = \frac{1}{3} - 3 + \mid 1 - 3. \frac{1}{3} \mid = - \frac{8}{3}\)

a) \(m = \sqrt{25 + 9}\) và \(n = \sqrt{25} + \sqrt{9}\).

Ta có \(m = \sqrt{34}\) và \(n = 5 + 3 = 8 = \sqrt{64}\).

Mà \(34 < 64\) nên \(m < n\).

b) \(y = \sqrt{49 - 16}\) và \(z = \sqrt{81} - \sqrt{9}\).

Ta có \(y = \sqrt{49 - 16} = \sqrt{33}\) và \(z = 9 - 3 \&\text{nbsp}; = 6 \&\text{nbsp}; = \sqrt{36}\).

Mà \(33 < 36\) nên \(y < z\).

a) A = \(\sqrt{36} . \left(\right. 3 \sqrt{4} - \sqrt{\frac{1}{9}} \left.\right) + 2\)

= \(6. \left(\right. 3.2 - \frac{1}{3} \left.\right) + 2\)

= \(36 - 2 + 2 = 36.\)

b) B = \(\sqrt{\frac{1}{9} + \frac{1}{16}}\)

= \(\sqrt{\frac{9 + 16}{9.16}}\)

= \(\sqrt{\frac{5^{2}}{3^{2} . 4^{2}}}\)

= \(\frac{5}{12}\).

c) C = \(\left(\right.\sqrt{\frac{1}{9}}+\sqrt{\frac{25}{36}}-\sqrt{\frac{49}{81}}\left.\right):\sqrt{\frac{441}{324}}\)

= \(\left(\right. \frac{1}{3} + \frac{5}{6} - \frac{7}{9} \left.\right) : \sqrt{\frac{2 1^{2}}{1 8^{2}}}\)

= \(\frac{7}{18} : \frac{7}{6}\)

= \(\frac{1}{3}\).

d) \(\sqrt{\left(\frac{- 2}{5}\right)^2}+\sqrt{1 , 44}-\sqrt{256}\)

= \(\frac{2}{5} + 1 , 2 - 16\)

= \(- \frac{72}{5}\)