Question

Numarul natural x care verifica egalitatea x la puterea a doua+x=90

Answer 1

$\displaystyle x^2+x=90 \\ x^2+x-90=0 \\ a=1,b=1,c=-90 \\ \Delta =b^2-4ac=1^2-4 \cdot 1 \cdot (-90)=1+360=361\ \textgreater \ 0 \\ x_1= \frac{-1+ \sqrt{361} }{2 \cdot 1} = \frac{-1+19}{2} = \frac{18}{2} =9 \in N \\ \\ x_2= \frac{-1- \sqrt{361} }{2 \cdot 1} = \frac{-1-19}{2} = \frac{-20}{2} =-10 \not \in N$