Question

Caluclati :

a).(  $\sqrt{2}$ + $\sqrt{3}$ ) ²

b). ( $\sqrt{2}$ + $\sqrt{3}$ ) ·( $\sqrt{2}$ - $\sqrt{3}$ )

c). ( $\sqrt{2}$ + $\sqrt{3}$ ) ² - ( $\sqrt{2}$ - $\sqrt{3}$ ) ²

Cine ma poate ajuta va rog ?

Answer 1

a) $(\sqrt{2} + \sqrt{3})^{2} = \sqrt{4} +2 \sqrt{6} + \sqrt{9} = 2 + 2 \sqrt{6} +3 = 5 + 2 \sqrt{6}$
b) $(\sqrt{2} + \sqrt{3})(\sqrt{2} - \sqrt{3}) = \sqrt{4} - \sqrt{9} = 2-3 = -1$
c)$(\sqrt{2} + \sqrt{3})^{2} -(\sqrt{2} - \sqrt{3})^{2} = \sqrt{4} + 2\sqrt{6} + \sqrt{9} - (\sqrt{4} - 2\sqrt{6} + \sqrt{9}) =$$2 + 2 \sqrt{6} + 3 - (2 - 2 \sqrt{6} + 3) = 5 + 2\sqrt{6} - ( 5 - 2\sqrt{6}) =$$5 + 2\sqrt{6} - 5 + 2\sqrt{6} = 4\sqrt{6}$