Question

1)Tính

a) √(2-√5)² +√(√5+1)²

b) (3+2√2)² + (1-√2)²

c) (1+√3)³

2) Tìm X

a) √9x² - 6x+1 =4

b) √x+1 + √4x+4 =9

3) Rút gọn

(3-x)² - √0,2 * √180a² với a >0 hoặc = 0

Answer 1

1)

a)\(\sqrt{\left(2-\sqrt{5}\right)^2}\) + \(\sqrt{\left(\sqrt{5}+1\right)^2}\)

= 2 - \(\sqrt{5}\) + \(\sqrt{5}\) +1 = 2 + 1 = 3

b) \(\left(3+2\sqrt{2}\right)^2+\left(1-\sqrt{2}\right)^2\)

=\(\left(3^2+2.3.2\sqrt{2}+2\sqrt{2}^2\right)+\left[1^2-2.1.\sqrt{2}+\left(\sqrt{2}\right)^2\right]\)

= (9 + 12\(\sqrt{2}\) + 8) + ( 1 - 2\(\sqrt{2}\) + 2)

= 9 + 12\(\sqrt{2}\) + 8 + 1 -2\(\sqrt{2}\) + 2

= 20 + 10\(\sqrt{2}\)

c) (1 + \(\sqrt{3}\))\(^3\)

=\(1^3+3.1^2.\sqrt{3}+3.1.\left(\sqrt{3}\right)^2+\left(\sqrt{3}\right)^3\)

= 1 + 3\(\sqrt{3}\) + 9 + 3\(\sqrt{3}\)

= 10 + 6\(\sqrt{3}\)