Question

one who give me answer with full solutions will be remarked the brainliest. ​

Answer 1

$\sqrt{a - 2 \sqrt{a - 1} } - \sqrt{a + 2 \sqrt{a - 1} }$

$\sqrt{a - 2 \sqrt{a - 1} } =$

$\red{\implies} \sqrt{( \sqrt{a - 1}){}^{2} - 2 \sqrt{a - 1} + {1}^{2} }$

$\red{ \implies} \sqrt{( { \sqrt{ a - 1} - 1)}^{2} }$

$\red{\implies \: \sqrt{a - 1} - 1 }$

$\rule{10cm}{0.05cm}$

$\red{\implies} \sqrt{( {\sqrt{a - 1})}^{2} + 2 \sqrt{a - 1} + 1 {}^{2} }$

$\red{ \implies}\sqrt{( \sqrt{ a - 1} + 1) {}^{2} } \:$

$\red{\implies \: \sqrt{a - 1} + 1 }$

$\rule{10cm}{0.05cm}$

$\sqrt{a - 2 \sqrt{a - 1} } - \sqrt{a + 2 \sqrt{a - 1} }$

$\red{ \implies}(\sqrt{a - 1} - 1 )- (\sqrt{a - 1} + 1)$

$\red{\implies} \sqrt{a - 1} - 1 - \sqrt{a - 1} - 1$

$\red{\implies \: -2 }$