Question

fie a=radical din 5-2 si b=radical din 5+2
a. determinati media aritmetica si media geometrica a celor 2 numere a si b.

descompunerea in factor a expresiei x la2- 4y la2

Answer 1

$a = \sqrt{5} - 2 \\ b = \sqrt{5} + 2 \\ ma = \frac{a + b}{2} = \\ = \frac{ \sqrt{5} - 2 + \sqrt{5} + 2}{2} = \frac{2 \sqrt{5} }{2} = \sqrt{5} \\ \\ mg = \sqrt{ab} = \sqrt{( \sqrt{5} - 2)( \sqrt{5} + 2) } = \sqrt{5 - 4} = 1$

${x}^{2} - 4 {y}^{2} = {x}^{2} - {(2y)}^{2} = (x - 2y)(x + 2y)$