Question

Найдите 1/а^2 +а^2, если известно, что 1/а-а=3

Answer 1

$\frac{1}{a}-a=3\\\\(\frac{1}{a}-a)^{2} =3^{2}\\\\\frac{1}{a^{2}}-2*\frac{1}{a}*a+a^{2}=9\\\\\frac{1}{a^{2}}-2+a^{2}=9\\\\\frac{1}{a^{2}} +a^{2}=11\\\\Otvet:\boxed{\frac{1}{a^{2}} +a^{2}=11}$