Question

a+1/a=3,calculeaza a^2+1/a^2​

Answer 1

Explicație pas cu pas:

a+1/a=3 => (a+1/a)^2=9 => a^2+2*a*1/a+1/a^2=9 =>

a^2+2+1/a^2=9 => a^2+1/a^2=7

Answer 2

Pentru a rezolva exercitiul ne vom folosi de un artificiu si vom ridica relatia la patrat.

$(a+\frac{1}{a}) ^{2}=3^{2}\\\\a^{2}+2a\frac{1}{a}+\frac{1}{a^{2}}=9\\\\a^{2}+2+\frac{1}{a^{2}}=9\\\\\\a^{2}+\frac{1}{a^{2}}=9-2\\\\a^{2}+\frac{1}{a^{2}}=7$