Question

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111 in baza x = 73 in baza 10
Ajutor​

Answer 1

 

$\displaystyle\bf\\\textbf{Transformam numarul 111 din baza x in baza 10.}\\\\111_x = x^2+x^1+x^0=73_{10}\\\\\textbf{Rezolvam ecuatia:}\\\\x^2+x^1+x^0=73\\\\x^2+x^1+1=73\\\\x^2+x^1+1-73=0\\\\x^2+x^1-72=0\\\\x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-1\pm\sqrt{1+4\cdot72}}{2}=\\\\=\frac{-1\pm\sqrt{1+288}}{2}=\frac{-1\pm\sqrt{289}}{2}=\frac{-1\pm17}{2}\\\\x_1=\frac{-1+17}{2}=\frac{16}{2}=\boxed{\bf8}\\\\x_2<0~~(solutie~eliminata)\\\\\boxed{\bf~x=8}\\\\\implies~\boxed{\bf111_8=73_{10}}$