Question

pls help me how to solve this. If x +1/x= 11. find x^2 +1/x^2 and x^4 +1/x^4

Answer 1

Answer:

x² + $\frac{1} {x^2}$ = 119

$x^{4} + \frac{1}{x^4}$ = 14159

Step-by-step explanation:

given x+ $\frac{1} {x}$ = 11

=> (x+ $\frac{1} {x}$)² = 11²

=> x² + 2 (x) ($\frac{1} {x}$) + ($\frac{1} {x}$)² = 121

=> x² + 2 + $\frac{1} {x^2}$ = 121

=> x² + $\frac{1} {x^2}$ = 121 - 2

=> x² + $\frac{1} {x^2}$ = 119 ----------------------- (1)

=> (x² + $\frac{1} {x^2}$)² = 119²

=> $(x^{2} )^2 + 2 (x^{2} )(\frac{1}{x^2} + (\frac{1}{x^2})^2$ = 14161

=> $x^{4} + 2 + \frac{1}{x^4}$ = 14161

=> $x^{4} + \frac{1}{x^4}$ = 14161 - 2

=> $x^{4} + \frac{1}{x^4}$ = 14159 ------------------- (2)

(1) & (2) are the required answers