Question

x-1/x =5 find the valu of x^2+1/x^2 and x^4+1/x^4
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Answer 1

Answer:

$x^{2}$ + $\frac{1}{x^{2} }$ = 27

$x^{4}$ + $\frac{1}{x^{4} }$ = 727

Step-by-step explanation:

x - $\frac{1}{x}$ = 5

=> $(x - \frac{1}{x}) ^{2}$ = $5^{2}$

=> $x^{2}$ - 2.x.$\frac{1}{x}$ + $\frac{1}{x^{2} }$ = 25

=> $x^{2}$ - 2 + $\frac{1}{x^{2} }$ = 25

=> $x^{2}$ + $\frac{1}{x^{2} }$ = 25 +2 = 27

=> $(x^{2} + \frac{1}{x}) ^{2} = 27^{2}$

=> $x^{4}$ + 2.$x^{2}$.$\frac{1}{x^{2} }$ + $\frac{1}{x^{4} }$ = $(30 - 3)^{2}$ = 900 - 2.30.3 + 9

=> $x^{4}$ + 2 + $\frac{1}{x^{4} }$ = 900 - 180 + 9

=> $x^{4}$ + $\frac{1}{x^{4} }$ = 729 - 2 = 727