Question

Va rog frumos sa ma ajutati. Imi pare rau de numele meu dar am nevoi de ajutor. Trebuie sa fac acest exercitiu : a+\frac{1}{a} = \frac{1}{a } . Si trebuie sa demonstrez ca a^{2} + \frac{1}{ a^{2} } = \frac{17}{4} . URGENT !

Answer 1

Salut,

$\left(a+\dfrac{1}a\right)^2=a^2+2\cdot a\cdot\dfrac{1}a+\dfrac{1}{a^2}=a^2+2+\dfrac{1}{a^2}\Rightarrow\\\\\Rightarrow a^2+\dfrac{1}{a^2}=\left(a+\dfrac{1}a\right)^2-2=\left(\dfrac{5}2\right)^2-2=\dfrac{25}4-2=\dfrac{17}4.$

Green eyes.