Question

a³+1=47
a² + 1/2 = ?
a

Answer 1

$\displaystyle \bigg (a^2 + \frac{1}{a^2} \bigg ) ^2 = a^4 + \frac{1}{a^4} +2 \\\\\\ \bigg (a^4 + \frac{1}{a^4} \bigg ) ^2 = \underbrace{a^8 + \frac{1}{a^8}}_{47} +2 \\\bigg (a^4 + \frac{1}{a^4} \bigg ) ^2 = 49 \\\\\\ \boldsymbol{a^4 + \frac{1}{a^4 } = 7} \\\\\\ \bigg (a^2 + \frac{1}{a^2} \bigg ) ^2 = \underbrace{a^4 + \frac{1}{a^4}}_ 7 +2 \\\\\\ \boxed{a^2 + \frac{1}{a^2} = 3 }$