Question

Calculati (a+b+c)-(a-b+c) , unde :
a=3V5-V20-4V3+V12
b=7V3-V48-2V5+V45
c=5V5-V27+5V3-V20

DAU COROANA
(V= radical)

Answer 1

$a = 3 \sqrt{5} - \sqrt{20} - 4 \sqrt{3} + \sqrt{12}$

$a = 3 \sqrt{5} - 2 \sqrt{5} - 4 \sqrt{3} + 2 \sqrt{3}$

$a = \sqrt{5} - 2 \sqrt{3}$

$b = 7 \sqrt{3} - \sqrt{48} - 2 \sqrt{5} + \sqrt{45}$

$b = 7 \sqrt{3} - 4 \sqrt{3} - 2 \sqrt{5} + 3 \sqrt{5}$

$b = 3 \sqrt{3} + \sqrt{5}$

$c = 5 \sqrt{5} - \sqrt{27} + 5 \sqrt{3} - \sqrt{20}$

$c = 5 \sqrt{5} - 3 \sqrt{3} + 5 \sqrt{3} - 2 \sqrt{5}$

$c = 3 \sqrt{5} + 2 \sqrt{3}$

$a + b + c = \sqrt{5} - 2 \sqrt{3} + 3 \sqrt{3} + \sqrt{5} + 3 \sqrt{5} + 2 \sqrt{3}$

$a + b + c = 5 \sqrt{5} + 3 \sqrt{3}$

$a - b + c = \sqrt{5} - 2 \sqrt{3} - (3 \sqrt{3} + \sqrt{5} ) + 3 \sqrt{5} + 2 \sqrt{3}$

$a - b + c = \sqrt{5} - 2 \sqrt{3} - 3 \sqrt{3} - \sqrt{5} + 3 \sqrt{5} + 2 \sqrt{3}$

$a - b + c = 3 \sqrt{5} - 3 \sqrt{3}$

$(a + b + c) - (a - b + c) = 5 \sqrt{5} + 3 \sqrt{3} - (3 \sqrt{5} - 3 \sqrt{3} )$

$(a + b + c) - (a - b + c) = 5 \sqrt{5} + 3 \sqrt{3} - 3 \sqrt{5} + 3 \sqrt{3}$

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