Toán rút gọn (căn( a+b+c+2 (căn ac+bc)))+(căn( a+b+c-2 (căn ac+bc))) 31/07/2021 By Claire rút gọn (căn( a+b+c+2 (căn ac+bc)))+(căn( a+b+c-2 (căn ac+bc)))
$\begin{array}{l}\sqrt{a + b +c + 2\sqrt{ac + bc}}+ \sqrt{a + b +c – 2\sqrt{ac + bc}}\\ = \sqrt{(a + b) +c + 2\sqrt{a + b}.\sqrt c}+ \sqrt{(a + b) +c – 2\sqrt{a + b}.\sqrt c}\\ = |\sqrt{a + b} + \sqrt c| + |\sqrt{a + b} – \sqrt c|\\ = \sqrt{a + b} + \sqrt c + |\sqrt{a + b} – \sqrt c|\\ =\left[\begin{array}{l}\sqrt{a + b} + \sqrt c + \sqrt{a + b} – \sqrt c \\\sqrt{a + b} + \sqrt c – (\sqrt{a + b} – \sqrt c)\end{array}\right.\\ = \left[\begin{array}{l}2\sqrt{a + b}\qquad ( a + b \geq c \geq 0)\\2\sqrt c\qquad \qquad(c > a + b \geq 0)\end{array}\right.\\\end{array}$ Trả lời
$\begin{array}{l}\sqrt{a + b +c + 2\sqrt{ac + bc}}+ \sqrt{a + b +c – 2\sqrt{ac + bc}}\\ = \sqrt{(a + b) +c + 2\sqrt{a + b}.\sqrt c}+ \sqrt{(a + b) +c – 2\sqrt{a + b}.\sqrt c}\\ = |\sqrt{a + b} + \sqrt c| + |\sqrt{a + b} – \sqrt c|\\ = \sqrt{a + b} + \sqrt c + |\sqrt{a + b} – \sqrt c|\\ =\left[\begin{array}{l}\sqrt{a + b} + \sqrt c + \sqrt{a + b} – \sqrt c \\\sqrt{a + b} + \sqrt c – (\sqrt{a + b} – \sqrt c)\end{array}\right.\\ = \left[\begin{array}{l}2\sqrt{a + b}\qquad ( a + b \geq c \geq 0)\\2\sqrt c\qquad \qquad(c > a + b \geq 0)\end{array}\right.\\\end{array}$