Question

if a= 9-4√5, find the value of (a-1/a)²​

Answer 1

Answer:

a=9-4root5

1/a=(1/9-4root5)×(9+4root5/9+4root5)

1/a=9+4root5

(a-1/a)^2

(9+4root5-9-4root5)^2

(0)^2

0

Answer 2

Answer:  The value of (a-1/a)²​ is 320

Step-by-step explanation:

a = 9 - 4√5

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

⇒ $\frac{1}{a} = \frac{1}{9-4\sqrt{5} }*\frac{9 +4\sqrt{5} }{9+4\sqrt{5} }$

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

⇒ $\frac{1}{a} = \frac{9 +4\sqrt{5} }{(81-80)}$

⇒ $\frac{1}{a} = 9 +4\sqrt{5}$

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

$(a-\frac{1}{a})^{2} = (-8\sqrt{5})^{2}$

$(a-\frac{1}{a})^{2} = 320$

#SPJ2