Question

If a=2+root 3 find a^3 /a^6 +3a^3 +1

Answer 1

Answer:

The answer is 94.00002.

Step-by-step explanation:

Given-

a= 2+ √3

Substitute 'a' in the equation

$\frac{ {a}^{3} }{ {a}^{6} + 3 {a}^{3} + 1 } \\ \\ = \frac{ ({2 + \sqrt{3} )}^{3} }{ ({2 + \sqrt{3} )}^{6} + 3( {2 + \sqrt{3} )}^{3} + 1 } \\ \\ = \frac{8 + ( \sqrt{3})^{3} }{(64 + { \sqrt{3} }^{6} ) + 3(8 + \sqrt{3}^{3}) + 1} \\ \\ = \frac{8 + ( \sqrt{3})^{3} }{(64 + { \sqrt{3} }^{6} ) +( 24 + \sqrt{3}^{3}) + 1} \\ \\ = \frac{ 1}{(64 + { \sqrt{3} }^{6} ) +3 + 1} \\ \\ = 64 + \sqrt{3}^{6} + 3 \\ \\ = 67 + (1.732051)^{6} \\ \\ = 67 + 27.00002\\ \\ = 94.00002$

We get the answer as 94.00002.

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