Question

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DAU COROANĂ ​

Answer 1

Explicație pas cu pas:

$\boxed {(a - b)(a + b) = {a}^{2} - {b}^{2}}$

$\boxed { {(a \pm b)}^{2} = {a}^{2} \pm 2ab + {b}^{2}}$

a)

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

b)

$(1 + 3\sqrt{2} )( 1 - 2\sqrt{2}) = 1 - 2 \sqrt{2} + 3 \sqrt{2} - 12 = \sqrt{2} - 11$

c)

$(3 + \sqrt{3} )(2 + \sqrt{3} ) = 6 + 3 \sqrt{3} + 2 \sqrt{3} + 3 = 9 + 5 \sqrt{3}$

d)

$( 2\sqrt{2} - \sqrt{3} )( 3\sqrt{2} - 3\sqrt{3} ) = 12 - 6 \sqrt{6} - 3 \sqrt{6} + 9 = 21 - 9 \sqrt{6} = 3(7 - 3 \sqrt{6})$

e)

$(\sqrt{5} - \sqrt{8} )(\sqrt{5} - 3\sqrt{2} ) = (\sqrt{5} - 2\sqrt{2} )(\sqrt{5} - 3\sqrt{2} ) = 5 - 3 \sqrt{10} - 2 \sqrt{10} + 12 = 17 - 5 \sqrt{10}$

f)

$( 2\sqrt{5} + 1)( 2\sqrt{5} - 1) = {(2 \sqrt{5} )}^{2} - 1 = 20 - 1 = 19$

g)

$( 5\sqrt{7} - \sqrt{13} )( \sqrt{13} + 5\sqrt{7} ) = ( 5\sqrt{7} - \sqrt{13} )(5\sqrt{7} + \sqrt{13}) = {(5 \sqrt{7} )}^{2} - {( \sqrt{13} )}^{2} = 175 - 13 = 162$

h)

$(2 \sqrt{5} + \sqrt{12})( \sqrt{12} - \sqrt{5}) - \sqrt{135} = (2 \sqrt{5} + 2\sqrt{3})( 2\sqrt{3} - \sqrt{5}) - 3\sqrt{15} = 4 \sqrt{15} - 10 + 12 - 2 \sqrt{15} - 3 \sqrt{15} = 2 - \sqrt{15}$