a = 9-4√5
a²+1/a²
=>a = 9-4√5.
=>1/a = 1/9-4√5. Rationalise
a² = 81 +80 -72√5 & 1/a² = 81 + 80 +72√5
=>a²+1/a²=81 +80 -72√5+ 81 + 80 +72√5
= 322
a = 9 - 4√5
a² + 1/a²
=> a = 9 - 4√5
=> 1/a = 1/9 - 4√5. Rationalise
=> 1/a = 9+4√5/81-80
=> 1/a = 9+4√5/1
a² = 81+80-71√5 & 1/a² = 81+80+72√5
=> a² +1/a² = 81+80-72√5+81+80+72√5
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Verified answer
Given
a = 9-4√5
To find
a²+1/a²
Solution
=>a = 9-4√5.
=>1/a = 1/9-4√5. Rationalise
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
Given
a = 9 - 4√5
To Find
a² + 1/a²
Solution
=> 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