Question

[(√5-2)/(√5+2)]-[(√5+2)/(√5-2)]=a+b√5​

Answer 1

Answer:a+b√5=0

Step-by-step explanation:[(√5-2)/(√5+2)]-[(√5+2)/(√5-2)]=a+b√5

(√5-2/√5+2-√5+2/√5-2)=a+b√5

(√5-2)^2-(√5+2)^2/(√5)^2-(√2)^2=a+b√5

5+4+4√5-(5+4+4√5)/5-4=a+b√5

9+4√5-9-4√5/3=a+b√5

a+b√5=0

Hope it will help you

Answer 2

$\huge\tt{\underline{\colorbox{teal}{\color{white}{↓ANSWER~:}}}}$

Given :

$\sf{ \dfrac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } - \dfrac{ \sqrt{5} + 2}{ \sqrt{5} - 2 } = a +b \sqrt{5} }$

According to the question,

$\begin{gathered}\begin{gathered} \leadsto\sf{ \dfrac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } - \dfrac{ \sqrt{5} + 2}{ \sqrt{5} - 2 } = a +b \sqrt{5} } \\ \\ \leadsto \sf{ \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2 } - \frac{ \sqrt{5} + 2}{ \sqrt{5} - 2} \times \frac{ \sqrt{5} + 2}{ \sqrt{5} + 2 } = a + b \sqrt{5} } \\ \\ \leadsto \sf{ \frac{ (\sqrt{5} - 2) {}^{2} }{5 - 4} - \frac{( \sqrt{5} + 2) {}^{2} }{5 - 4} = a + b \sqrt{5} } \\ \\ \leadsto \sf{ \dfrac{5 - 4 \sqrt{5} + 4 - \big(5 + 4 \sqrt{5} + 4 \big)}{1} = a + b \sqrt{5} } \\ \\ \leadsto \sf{ \cancel5 - 4 \sqrt{5} + \cancel4 - \cancel 5 - \cancel 4 \sqrt{5 } - 4 = a + b \sqrt{5} } \\ \\ \leadsto \sf{ - 8 \sqrt{5} = a + b \sqrt{5} } \\ \\ { \underline{ \boxed{ \bold \red{a = 0 \: }}}} \: \: { \underline{ \boxed{ \bold \red{b = - 8 \sqrt{5} }}}}\end{gathered} \end{gathered}$

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