Question

Daca
$a \ - \frac{1}{a} = \frac{3}{2}$
Arătați că
${a}^{2} + \frac{1}{a {}^{2} } = \frac{17}{4}$

Answer 1

a-(1/a)=3/2|*²

a²-(1/a²)=9/4

a²+(1/a²)-2=9/4

a²+(1/a²)=2+(9/4)

a²+(1/a²)=(8+9)/4

a²+(1/a²)=17/4

Bafta!