Question

x^2+3x+1=0 then what is the value of x^6+1/x^6?​

Answer 1

Answer:

$\huge\underline{ \underline{ \red{your \: \: answer}}}$

Step-by-step explanation:

$\sf\pink{ {x}^{2} + 3x + 1 } \\ \sf\pink{ = > x = \frac{ - b±\sqrt{ {b}^{2} - 4a } }{2a} } \\ \sf\pink{x = \frac{ - 3± \sqrt{ { - 3}^{2} - 4 \times 1 \times 1 } }{2 \times 1} } \\ \sf\pink{ = > x = \frac{ - 3±\sqrt{9 - 4} }{2} } \\ \sf\pink{ = > x = \frac{ - 3±\sqrt{5} }{2} } \\ \sf\pink{ = > x = \frac{ - 3±\sqrt{5} }{2} } \\ \sf\green{ = > x = \frac{ - 3 + \sqrt{5} }{2} and \: x = \frac{ - 3 - \sqrt{5} }{2} } \\ \sf\pink{ {x}^{6} + \frac{1}{ {x}^{6} } = ?} \\ \sf\pink{ = > \frac{ - 3 + \sqrt{5} }{2} + \frac{1}{ \frac{ - 3 + \sqrt{5} }{2} } } \\ \sf\pink{ = > \frac{ - 3 + \sqrt{5} }{2} \times \frac{2}{ - 3 + \sqrt{5} } } \\ \sf\pink{ = > \frac{ {( - 3 + \sqrt{5} )}^{2} + {2}^{2} }{2 \times (- 3 + \sqrt{5} )} } \\ \sf\pink{ = > \frac{9 + 5 - 6 \sqrt{5} + 4 }{2 \times ( - 3 + \sqrt{5} )}} \\ \sf\pink{ = > \frac{18 - 6 \sqrt{5} }{2 \times ( - 3 + \sqrt{5} )} } \\ \sf\pink{ = > \frac{ - 6( - 3 + \sqrt{5} )}{2( - 3 + \sqrt{5} )} } \\ \sf\pink{ = > \frac{ - 6}{2} } \\ \sf\pink{ = > 3} \\ \large\boxed{ \fcolorbox{red}{pink}{hope \: it \: help \: you}}$