Question

\[\text {Let,}~~ \text{x} = x - [x]~.~ \text{If }~{\{a}^{-1}\} = {\{a^2}\}~ \text {and}~ 2 < a^2 < 3,~ \text{then} a^{12} - 144*a^{-1} = ?\]

Answer 1

I know that,

\([a^2] = 2\)

Answer 2

Sorry couldn't get the correct latex.

Answer 3

\[\text {Let,}~~ \text{x} = x - [x]~.~ \text{If }~{{a}^{-1}} = {{a^2}}~ \text {and}~ 2 < a^2 < 3,~ \text{then} a^{12} - 144*a^{-1} = ?\]

Answer 4

{a^{-1} = a^{2}}

THis should be present

Answer 5

\(\text {Let,}~~ \text{x} = x - [x]~.~ \text{If }~{\{a}^{-1}\} = {\{a^2}\}~ \text {and}~ 2 < a^2 < 3,~ \text{then} a^{12} - 144*a^{-1} = ?\)

Answer 6

This is the correct question.

Answer 7

\(\text {Let,}~~ \text{{x}} = x - [x]~.~ \\ \text{If }~{\{a}^{-1}\} = {\{a^2}\}~ \text {and}~ 2 < a^2 < 3,~ \text{then } a^{12} - 144*a^{-1} = ?\)

Answer 8

I think you mean that ?

Answer 9

yes

Answer 10

I got two "solutions" to that...

Answer 11

[a] = 1
[1/a] = 0

{a^{-1}} = 1/a
{a^2} = a^2-1

Answer 12

1/a = a^2 - 1

Answer 13

Is this the golden number???

Answer 14

its a cubic^