Question

Daca a-1/a=3,calculati:a^2+1/a^2 si a^4+1/a^4.

Answer 1

$\frac{a - 1}{a} = 3 \: rezulta \: a - 1 = 3a \: rezulta \: a - 3a =1 \: rezulta \: - 2a = 1 \: rezulta \: a = - \frac{1}{2}$

$\frac{( - \frac{1}{2} ) {}^{2} + 1 }{ ( - \frac{1}{2}) {}^{2} } = \frac{ \frac{1}{4} + 1}{( - \frac{1}{2} ) {}^{2} } = \frac{ \frac{5}{4} }{( - \frac{1}{2}) {}^{2} } = \frac{5}{4 \times ( - \frac{1}{2} ) {}^{2} } = \frac{5}{4 \times ( \frac{1}{2}) {}^{2} } = \frac{5}{4 \times \frac{1}{4} } = \frac{5}{1} = 5$

$\frac{( - \frac{1}{2} ) {}^{4} + 1}{( - \frac{1}{2} ) {}^{4} } = \frac{ \frac{1}{16} + 1}{( - \frac{1}{2}) {}^{4} } = \frac{ \frac{17}{16} }{( - \frac{1}{2} ) {}^{4} } = \frac{17}{16 \times ( - \frac{1}{2} ) {}^{4} } = \frac{17}{16 \times ( \frac{1}{2}) {}^{4} } = \frac{17}{16 \times \frac{1}{16} } = \frac{17}{1} = 17$