Question

x^2+1/x^2=79,then find the value of x^3+1/x^3

Answer 1

$\large{\mathfrak{HELLO \: \: DEAR,}}$

$\mathit{WE \: \: KNOW \: \: THAT:-} \\ \\ \mathbf{(a + b)^2 = (a^2 + b^2 + 2ab)} \\ \\ \mathit{\underline{NOW,}} \\ \\ \mathbf{put a = x , \: \: b = \frac{1}{x}} \\ \\ \mathit{(x + \frac{1}{x})^2 - 2* x *\frac{1}{x} = 79}\\ \\ \mathit{(x + \frac{1}{x})^2 = 81}\\ \\ \mathit{(x + \frac{1}{x})= 9}\\ \\ \mathit{IN \: \: CUBING \: \: BOTH \: \: SIDE:-} \\ \\ \mathit{WE \: \: GET,} \\ \\ \mathit{x^3 + \frac{1}{x^3} + 3x * \frac{1}{x}(x + \frac{1}{x}) = 719}\\ \\ \mathit{(x^3 + \frac{1}{x^3}) = 719 - 3(9)}\\ \\ \mathit{(x^3 + \frac{1}{x^3})=692}$
$\large{\mathit{\underline{I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}}}$