Question

How to Factorize x^4+x^2+1

Answer 1

Solution:-

given by:-

${x}^{4} + {x}^{2} + 1 \\ put \: {x}^{2} = y \\ we \: have \\ {y}^{2} + y + 1 \\ by \: formula \: \\ \frac{ - b( + - ) \sqrt{ {b}^{2} - 4ac } }{2a} \\ \frac{ - 1( + - ) \sqrt{1 - 4} }{2} \\ \frac{ - 1( + - ) \sqrt{3} }{2} \\ (y + \frac{1 + \sqrt{3} }{2} ) \\ (y + \frac{1 - \sqrt{3} }{2} ) \\ put \: y \: value \\ ( {x}^{2} + \frac{1 + \sqrt{3} }{2} ) ( {x}^{2} + \frac{1 - \sqrt{3} }{2} )$