Question

what is the psychology behind the luck?

Answer 1

Answer:

Lucky people consistently search for new opportunities or create better opportunities. They respect and respond to their intuition or luck hunches and act upon. They always dream and desire for success and try to fulfill them

Explanation:

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Answer 2

Explanation:

$\qquad$❏$\sf\red{{ \dfrac{1}{ \sqrt{7} + \sqrt{6} - \sqrt{13} } }}$

Let:-

$\qquad$☀️ $\sf { \sqrt{7} + \sqrt{6} = a }$

$\qquad$☀️ $\sf { \sqrt{13} = b }$

$\qquad$❏ To rationalise the denominator, we'll have to multiply the denominator and the numerator by its rationalising factor. As we supposed (√7 + √6) as a and √13 as b, so the denominator is like ( a - b ). We know that rationalising factor of $\sf{ (a -b)}$ is $\sf { (a + b)}$. Therefore, the rationalising factor of $\bigg ( \sf { \dfrac{1}{\sqrt{7} + \sqrt{6} - \sqrt{13} } } \bigg )$ is $( \sf { \sqrt{7} + \sqrt{6} + \sqrt{13} } )$.

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$\qquad\leadsto\quad \sf { \dfrac{1}{ \sqrt{7} + \sqrt{6} - \sqrt{13} } \times \dfrac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{ \sqrt{7} + \sqrt{6} + \sqrt{13} } }$

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$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{ { \big( \sqrt{7} + \sqrt{6} \big ) }^{2} - {( \sqrt{ 13} )}^{2} } }$

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$\qquad$❏$(a - b)(a + b) = a² - b² </p><p></p><p>[tex]\qquad\leadsto\quad \tt { \dfrac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{ {( \sqrt{7}) }^{2} + { (\sqrt{6}) }^{2} + 2( \sqrt{7} \times \sqrt{6} ) } - {( \sqrt{13}) }^{2} }$

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$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{ 7 + 6 + 2( \sqrt{42} ) - 13 } }$

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$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{ \cancel{ 13} + 2( \sqrt{42} ) \cancel{- 13} }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{ 2( \sqrt{42} ) }}$

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$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{7} + \sqrt{6} + \sqrt{13} }{ 2( \sqrt{42} ) } \times \dfrac{ \sqrt{42} }{ \sqrt{42} } }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{42} (\sqrt{7} )+ \sqrt{42} (\sqrt{6} )+ \sqrt{42(} \sqrt{13}) }{ \sqrt{42} (2 \sqrt{42}) } }$

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$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{294} + \sqrt{252} + \sqrt{546} }{ 2 \times 42 } }$

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$\qquad\leadsto\quad \sf { \dfrac{ \sqrt{294} + \sqrt{252} + \sqrt{546} }{ 84} }$

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$\qquad\leadsto\quad \sf { \dfrac{ 7\sqrt{6} + 6\sqrt{7} + \sqrt{546} }{ 84} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\leadsto\quad \tt { \dfrac{7\sqrt{6}}{84} + \dfrac{6\sqrt{7} }{84} + \dfrac{\sqrt{546} }{ 84} }$

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$\qquad\leadsto\quad \sf\red{ \boxed{ \tt{ \dfrac{\sqrt{6}}{12} + \dfrac{\sqrt{7} }{14} + \dfrac{\sqrt{546} }{ 84} } }}$