Question

Please answer it’s urgent the maths question

Answer 1

Given

a = 9-4√5

To find

a²+1/a²

Solution

• Step 1:- Rationalise the value to get 1/a
• Now add the values of both
• with their squares

=>a = 9-4√5.

=>1/a = 1/9-4√5. Rationalise

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

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

$\sf\red{\rightarrow\dfrac{1}{a}=\frac{9+4\sqrt{5}}{1}}$

Now adding both

a² = 81 +80 -72√5 & 1/a² = 81 + 80 +72√5

=>a²+1/a²=81 +80 -72√5+ 81 + 80 +72√5

= 322

Answer 2

Given

a = 9 - 4√5

To Find

a² + 1/a²

Solution

• Step 1 = Rationalise The Value To Get 1/a²
• Now Add The Value Of Both
• With Their Squares

=> a = 9 - 4√5

=> 1/a = 1/9 - 4√5. Rationalise

=> 1/a = 1/9 - 4√5 × 9+4√5/9+4√5

=> 1/a = 9+4√5/81-80

=> 1/a = 9+4√5/1

Now Adding Both

a² = 81+80-71√5 & 1/a² = 81+80+72√5

=> a² +1/a² = 81+80-72√5+81+80+72√5

=> 322