Question

x + \frac{1}{x} = 3 \\ \\ \\ (x + \frac{1}{x})^2 = 3^2 \\ \\ = x^2 + \frac{1}{x^2} + (2 \times x \times \frac{1}{x}) = 9 \\ \\ = x^2 + \frac{1}{x^2} + 2 = 9 \\ \\ x^2 + \frac{1}{x^2} = 9 - 2 = 7 \\ \\ \\ (x^2 + \frac{1}{x^2})^2 = 7^2 \\ \\ = x^4 + \frac{1}{x^4} + (2 \times x^2 \times \frac{1}{x^2}) = 49 \\ \\ = x^4 + \frac{1}{x^4} + 2 = 49 \\ \\ x^4 + \frac{1}{x^4} = 49 - 2 = 47 \\ \\ \\

\\ \\ \\ (x + \frac{1}{x})^6 = 3^6 \\ \\ = x^6 + (6 \times x^5 \times \frac{1}{x}) + (15 \times x^4 \times \frac{1}{x^2}) + (20 \times x^3 \times \frac{1}{x^3}) + (15 \times x^2 \times \frac{1}{x^4}) + (6 \times x \times \frac{1}{x^5}) + \frac{1}{x^6} = 729 \\ \\ = x^6 + 6x^4 + 15x^2 + 20 + \frac{15}{x^2} + \frac{6}{x^4} + \frac{1}{x^6} = 729 \\ \\ = x^6 + 6(x^4 + \frac{1}{x^4}) + 15(x^2 + \frac{1}{x^2}) + 20 + \frac{1}{x^6} = 729 \\ \\ = x^6 + (6 \times 47) + (15 \times 7) + 20 + \frac{1}{x^6} = 729 \\

\\ \\ \\ = x^6 + 282 + 105 + 20 + \frac{1}{x^6} = 729 \\ \\ = x^6 + \frac{1}{x^6} + 407 = 729 \\ \\ \\ x^6 + \frac{1}{x^6} = 729 - 407 \\ \\ = x^6 + \frac{1}{x^6} = 322

∴ 322 is the answer.


Explain using this on how to get x power 12 plus x by 1 by x power 12.

Answer 1

$</p><p></p><p>x + \frac{1}{x} = 3 \\ \\ \\ (x + \frac{1}{x})^2 = 3^2 \\ \\ = x^2 + \frac{1}{x^2} + (2 \times x \times \frac{1}{x}) = 9 \\ \\ = x^2 + \frac{1}{x^2} + 2 = 9 \\ \\ x^2 + \frac{1}{x^2} = 9 - 2 = 7 \\ \\ \\ (x^2 + \frac{1}{x^2})^2 = 7^2 \\ \\ = x^4 + \frac{1}{x^4} + (2 \times x^2 \times \frac{1}{x^2}) = 49 \\ \\ = x^4 + \frac{1}{x^4} + 2 = 49 \\ \\ x^4 + \frac{1}{x^4} = 49 - 2 = 47 \\ \\ \\ </p><p></p><p>\\ \\ \\ (x + \frac{1}{x})^6 = 3^6 \\ \\ = x^6 + (6 \times x^5 \times \frac{1}{x}) + (15 \times x^4 \times \frac{1}{x^2}) + (20 \times x^3 \times \frac{1}{x^3}) + (15 \times x^2 \times \frac{1}{x^4}) + (6 \times x \times \frac{1}{x^5}) + \frac{1}{x^6} = 729 \\ \\ = x^6 + 6x^4 + 15x^2 + 20 + \frac{15}{x^2} + \frac{6}{x^4} + \frac{1}{x^6} = 729 \\ \\ = x^6 + 6(x^4 + \frac{1}{x^4}) + 15(x^2 + \frac{1}{x^2}) + 20 + \frac{1}{x^6} = 729 \\ \\ = x^6 + (6 \times 47) + (15 \times 7) + 20 + \frac{1}{x^6} = 729 \\ </p><p></p><p>\\ \\ \\ = x^6 + 282 + 105 + 20 + \frac{1}{x^6} = 729 \\ \\ = x^6 + \frac{1}{x^6} + 407 = 729 \\ \\ \\ x^6 + \frac{1}{x^6} = 729 - 407 \\ \\ = x^6 + \frac{1}{x^6} = 322 </p><p></p><p>∴ 322 is the answer.</p><p></p><p>Explain using this on how to get x power 12 plus x by 1 by x power 12$

hope it helps you please mark me as brainliest