Question

√5-2/√5+2-√5+2/√5-2=a+b√5
find a and b​

Answer 1

Answer:

i hope this helps you

Step-by-step explanation:

Answer 2

Given :

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

To find :

• The value of a and b

According to the question,

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