Đáp án:
$A = -2\sqrt[]{x}$
$B = x + 4$
$C = -3\sqrt[]{x}$
Giải thích các bước giải:
$a. A = 5\sqrt[]{4x} - 3\sqrt[]{\frac{100x}{9}} - \frac{4}{x}×\sqrt[]{\frac{x^{3}}{4}}$
$A = 5×2\sqrt[]{x} - 3×\frac{10}{3}×\sqrt[]{x} - \frac{4}{x}×\frac{|x|\sqrt[]{x}}{2}$
$A = 10\sqrt[]{x} - 10\sqrt[]{x} - \frac{2}{x}×x\sqrt[]{x}$ $( x > 0 ⇒ |x| = x )$
$A = -2\sqrt[]{x}$
$b. B = \frac{1}{3}\sqrt[]{9+6x+x^{2}} + \frac{4x}{3} + 5$
$B = \frac{1}{3}\sqrt[]{(x+3)^{2}} + \frac{4x}{3} + 5$
$B = \frac{1}{3}| x + 3 | + \frac{4x}{3} + 5$
$B = \frac{1}{3}×( - x - 3 ) + \frac{4x}{3} + 5$ $( x ≤ -3 ⇒ x + 3 ≤ 0 ⇒ | x + 3 | = - x - 3 )$
$B = \frac{-x+4x}{3} - 1 + 5$
$B = x + 4$
$c. C = 4\sqrt[]{25x} - \frac{15}{2}×\sqrt[]{\frac{16x}{9}} - \frac{2}{x}×\sqrt[]{\frac{169x^{3}}{4}}$
$C = 4×5\sqrt[]{x} - \frac{15}{2}×\frac{4}{3}×\sqrt[]{x} - \frac{2}{x}×\frac{13}{2}×|x|\sqrt[]{x}$
$C = 20\sqrt[]{x} - 10\sqrt[]{x} - \frac{13}{x}×x\sqrt[]{x}$ $( x > 0 ⇒ |x| = x )$
$C = 10\sqrt[]{x} - 13\sqrt[]{x}$
$C = -3\sqrt[]{x}$
