Question

if x+1/x =√5 find the value of x^2+1/x^2 and x^4+1/x^4

Answer 1

Answer:

$x + \frac{1}{x} = \sqrt{5} \\ x {}^{2} + \frac{1}{x {}^{2} } = (x + \frac{1}{x}) {}^{2} - 2 \times x \times \frac{1}{x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (\sqrt{5} ) { }^{2} - 2 = 5 - 2 = 3 \\ x {}^{4} + \frac{1}{x {}^{4} } = (x {}^{2} + \frac{1}{x {}^{2} } ) - 2 \times x {}^{2} \times \frac{1}{x {}^{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > 3 {}^{2} - 2 = 9 - 2 = 7$