Question

Calculati: (2√3-1)^2=?

Answer 1

(2√3-1)² = (2√3)² + 2*2√3*(-1) + (-1)² = 4*3 - 4√3 + 1 = 12 - 4√3 + 1 = 13 - 4√3

Am folosit formula (a-b)² = a² - 2ab + b², unde a = 2√3 si b = -1.

Answer 2

$1) \\ \\ {(2 \sqrt{3} - 1) }^{2} = \\ \\ {(2 \sqrt{3}) }^{2} - 2 \times 2 \sqrt{3} \times 1 + {1}^{2} = \\ \\ 4 \times 3 - 4 \sqrt{3} + 1 = \\ \\ 12 - 4 \sqrt{3} + 1 = \\ \\ 13 - 4 \sqrt{3}$

$2) \\ \\ {(2 \sqrt{3} - 1) }^{2} = \\ \\ {(2 \sqrt{3}) }^{2} - 2 \times 2 \sqrt{3} + 1 = \\ \\ {2}^{2} { \sqrt{3} }^{2} - 2 \times 2 \sqrt{3} + 1 = \\ \\ 4 \times 3 - 2 \times 2 \sqrt{3} + 1 = \\ \\ 12 - 4 \sqrt{3} + 1 = \\ \\ 13 - 4 \sqrt{3}$