Question

can anyone solve it pls​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{The given expression is }\dfrac{\sqrt5 + 2}{\sqrt5 - 2} - \dfrac{\sqrt5 -2}{\sqrt5 + 2}$

       $\text{Simplifying...}$

$\implies \dfrac{(\sqrt5 + 2)^{2} - (\sqrt5 - 2)^{2}}{(\sqrt5 - 2)(\sqrt5 + 2)}$

       $\text{We know the following identities:}$

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

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

       $(a+b)(a-b) = a^{2} - b^{2}$

$\implies \dfrac{(\sqrt5)^{2} + (2)^{2} + 2(\sqrt5)(2)- [(\sqrt5)^{2} + (2)^{2}-2(\sqrt5)(2)]}{(\sqrt5)^{2} - (2)^{2}}$

       $\text{Simplifying...}$

$\implies \dfrac{5 + 4 + 4\sqrt5- (5 + 4 - \s4\sqrt5)}{5 - 4}$

       $\text{Simplifying...}$

$\implies \dfrac{5 + 4 + 4\sqrt5-5 - 4 + 4\sqrt5}{1}$

       $\text{Simplifying...}$

$\implies \boxed{8\sqrt5}$

Answer 2

Answer:

hey here is your answer

pls mark it as brainliest pls

Step-by-step explanation:

$so \: here \: \\ \frac{ \sqrt{5} + 2 }{ \sqrt{5} - 2 } \: \: - \: \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } \\ \\ = \frac{ (\sqrt{5} + 2 )( \sqrt{5} + 2 ) - ( \sqrt{5} - 2)( \sqrt{5} - 2 )}{( \sqrt{5} + 2 )( \sqrt{5} - 2 )} \\ \\ = \frac{( \sqrt{5} + 2 ) {}^{2} \: - ( \sqrt{5} - 2 ) {}^{2} }{( \sqrt{5}) {}^{2} - (2) {}^{2} } \\ \\ = \frac{5 + 4 + 4 \sqrt{5} - (5 + 4 - 4 \sqrt{5} )}{5 - 4} \\ \\ = \frac{9 + 4 \sqrt{5} - 9 + 4 \sqrt{5} }{1} \\ \\ = 4 \sqrt{5} + 4 \sqrt{5} \\ \\ = 8 \sqrt{5}$