Question

If x+1/x=√5, Find The Value of:-
i. x²+1/x² And ii. x⁴+1/x⁴

Please, It's Urgent,​

Answer 1

SOLUTION :

$x {}^{} + \frac{1}{x {}^{} } = \sqrt{5} \\ \\ squaring \: on \: both \: sides \\ \\ = > x {}^{2} + \frac{1}{x {}^{2} } + 2x. \frac{1}{x} = 5 \\ \\ (a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab \: \\ \\ = > x {}^{2} + \frac{1}{x {}^{2} } + 2 = 5 \\ \\ = > x {}^{2} + \frac{1}{x {}^{2} } = 3 - - (1) \\ \\ squaring \: on \: both \: sides \\ \\ = > x {}^{4} + \frac{1}{ {x}^{4} } + 2.x {}^{2} . \frac{1}{x {}^{2} } = 9 \\ \\ = > x {}^{4} + \frac{1}{x {}^{4} } + 2 = 9 \\ \\ = > x {}^{4} + \frac{1}{x {}^{4} } = 7$

HOPE IT HELPS !!!!

Answer 2

x+1/x = 5

(x+1/x)² = x²+1/x²+2

(5)² = x²+1/x²+2

25-2 = x²+1/x² => 23

(x²+1/x²)² = x⁴+1/x⁴+2

(23)² = x⁴+1/x⁴+2

529-2 = x⁴+1/x⁴

527 = x⁴+1/x⁴

hope this helps