Question

a^2-5a+1=0 and a≠0 ,find a^2+1/a^2​

Answer 1

Step-by-step explanation:

${a}^{2} - 5a + 1 = 0 \\ a = \frac{5}{2} + \frac{ \sqrt{25 - 4} }{2} \\ a = \frac{5 + \sqrt{21} }{2} \\ or \\ a = \frac{5 - \sqrt{21} }{2}$

${a}^{2} = ( { \frac{5 + \sqrt{21} }{2} })^{2} = \frac{46 + 10 \sqrt{21} }{4} \\ or \\ \frac{46 - 10 \sqrt{21} }{4} \\ \frac{1}{ {a}^{2} } = \frac{4}{46 + 10 \sqrt{21} }$

Now simply add it