Solve the following mathematical problems:

Find the value of $x^{6} + \frac{1}{x^{6}},$ if $x + \frac{1}{x} = 3$ (Algebraic Formula)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$(x + \frac{1}{x}) = 3 N o w, (x^{6} + \frac{1}{x^{6}}) = {(x^{2})}^{3} + {(\frac{1}{x^{2}})}^{3} = {(x^{2} + \frac{1}{x^{2}})}^{3} - 3 \times x^{2} \times \frac{1}{x^{2}} (x^{2} + \frac{1}{x^{2}}) = {(x^{2} + \frac{1}{x^{2}})}^{3} - 3 (x^{2} + \frac{1}{x^{2}}) = {\{{(x + \frac{1}{x})}^{2} - 2 \times x \times \frac{1}{x}\}}^{3} - 3 \{{(x + \frac{1}{x})}^{2} - 2 \times x \times \frac{1}{x}\} = {\{{(3)}^{2} - 2\}}^{3} - 3 (9 - 2) = {(7)}^{3} - 3 \times 7 = 343 - 21 = 322 a n s .$