Question

if b=2+√5/2-√5 and a=2-√5/2+√5 then find a a=2+√5/2-√5-2-√5/2+√5
please solve this​

Answer 1

Answer:

144√5

Step-by-step explanation:

• Simplifying b :-

$\implies b=\dfrac{2-\sqrt5}{2+\sqrt5}$

Multiply as well as divide by $\dfrac{2-\sqrt5}{2-\sqrt5}$

$\implies b=\dfrac{2-\sqrt5}{2+\sqrt5}\times\dfrac{2-\sqrt5}{2-\sqrt5}\\\\\\\implies b=\dfrac{(2-\sqrt5)^2}{(2+\sqrt5)(2-\sqrt5)}\\\\\\\implies b=\dfrac{4+5-4\sqrt5}{2^2-\sqrt5^2}\\\\\\\implies b=\dfrac{9-4\sqrt5}{4-5}\\\\\\\implies b=4\sqrt5-9$

• Simplifying a :-

Multiply as well as divide by $\dfrac{2+\sqrt5}{2+\sqrt5}$

$\implies a=\dfrac{2+\sqrt5}{2-\sqrt5}\times\dfrac{2+\sqrt5}{2+\sqrt5}\\\\\\\implies a=\dfrac{(2+\sqrt5)^2}{(2-\sqrt5)(2+\sqrt5)}\\\\\\\implies a=\dfrac{4+5+4\sqrt5}{2^2-\sqrt5^2}\\\\\\\implies a=\dfrac{9+4\sqrt5}{4-5}\\\\\\\implies a=4\sqrt5-9$

Hence,

= > a^2 - b^2

= > ( - 4√5 - 9 )^2 - ( 4√5 - 9 )^2

= > (4√5)^2 + (9)^2 + 72√5 - (4√5)^2 - (9)^2 + 72√5

= > 144√5

Answer 2

Answer:

144√5

Step-by-step explanation:

dont have one did it and got a 100%