Question

G. 1f x+1/x=
$\sqrt5$
, find the value of X2 + 1/X2 and X⁴ + 1/x⁴.​

Answer 1

Answer:

x²+$\frac{1} {x^2}$ = 3

x⁴+$\frac{1} {x^4}$ = 7

Step-by-step explanation:

given, x+$\frac{1} {x}$ = √5

=>  (x+$\frac{1} {x}$)² = (√5)²

=>  x²+($\frac{1} {x}$)²+2x($\frac{1} {x}$ )= 5

=>  x²+$\frac{1} {x^2}$ = 5-2

=>  x²+$\frac{1} {x^2}$ = 3

on squaring again,

=>  (x²+$\frac{1} {x^2}$)² = 3²

=>  (x²)²+($\frac{1} {x^2}$)²+ 2 (x²)($\frac{1} {x^2}$) = 9

=>  x⁴+$\frac{1} {x^4}$+ 2 = 9

=>  x⁴+$\frac{1} {x^4}$ = 9 - 2

=>  x⁴+$\frac{1} {x^4}$ = 7