Question

$a = \sqrt{11 + 4\sqrt{7} } \\b = \sqrt{11 - 4\sqrt{7} }$

A) a × b =
B) aratati ca $(a - b)^{2} = 16$

Answer 1

$a = \sqrt{11 + 4 \sqrt{7} }$

$b = \sqrt{11 - 4 \sqrt{7} }$

$A)a \times b = \sqrt{11 + 4 \sqrt{7} } \times \sqrt{11 - 4 \sqrt{7} }$

$a \times b = \sqrt{(11 + 4 \sqrt{7} )(11 - 4 \sqrt{7} )}$

$a \times b = \sqrt{ {11}^{2} - {(4 \sqrt{7} )}^{2} }$

$a \times b = \sqrt{121 - 112}$

$a \times b = \sqrt{9}$

$a \times b = 3$

$B) {(a - b)}^{2} = 16$

${(a - b)}^{2} = {( \sqrt{11 + 4 \sqrt{7} } - \sqrt{11 - 4 \sqrt{7} }) }^{2}$

${(a - b)}^{2} = {( \sqrt{11 + 4 \sqrt{7} } )}^{2} - 2 \sqrt{(11 + 4 \sqrt{7} )(11 - 4 \sqrt{7} )} + {( \sqrt{11 - 4 \sqrt{7} }) }^{2}$

${(a - b)}^{2} = 11 + 4 \sqrt{7} - 2 \times 3 + 11 - 4 \sqrt{7}$

${(a - b)}^{2} = 4 \sqrt{7} - 4 \sqrt{7} + 11 + 11 - 6$

${(a - b)}^{2} = 22 - 6$

${(a - b)}^{2} = 16$