Question

if a=9-4√5 ,find the value of a-1/a
i got the answer as 0 but i don't think my answer is correct so anyone please help me to do this it's a request
the answer which I got is this (refer the image)​

Answer 1

You did everything correct but you messed up at the end

Here is full solution hope it helps

Answer:

$a=9-4\sqrt{5}$

$\dfrac{1}{a}=\dfrac{1}{9-4\sqrt{5} }$

$\dfrac{1}{a}=\dfrac{1}{9-4\sqrt{5} }\times \dfrac{9+4\sqrt{5} }{9+4\sqrt{5} }$

$\dfrac{1}{a}=\dfrac{9+4\sqrt{5} }{(9-4\sqrt{5})(9+4\sqrt{5})}$

$\dfrac{1}{a}=\dfrac{9+4\sqrt{5} }{9^2-(4\sqrt{5})^2 }$

$\dfrac{1}{a}=\dfrac{9+4\sqrt{5} }{81-80}$

$\dfrac{1}{a}={9+4\sqrt{5}$

$a-\dfrac{1}{a} = (9-4\sqrt{5})- (9+4\sqrt{5})$

$a-\dfrac{1}{a} = 9-4\sqrt{5}- 9-4\sqrt{5}$

$a-\dfrac{1}{a} = -4\sqrt{5}-4\sqrt{5}$

$a-\dfrac{1}{a} = -8\sqrt{5}$

$\mathrm{rohangupta0424}$