Question

If $a^2-5a-1=0$, then find $a+\frac{1}{a}$

• A. $\pm \sqrt{59}$
• B. $\pm \sqrt{39}$
• C. $\pm \sqrt{29}$
• D. $\pm \sqrt{19}$

Answer 1

The correct option is C $\pm \sqrt{29}$

$a^2-5a-1=0$

$=>a^2-1=5a$

$=>a-\frac{1}{a}=5$

Squaring both sides, we get

$=>a^2+\frac{1}{a^2}-2a\times \frac{1}{a}=25$

$=>a^2+\frac{1}{a^2}=25+2$

$=>a^2+\frac{1}{a^2}=27$

Now,

$(a+\frac{1}{a}{)}^2=a^2+\frac{1}{a^2}+2a\times \frac{1}{a}$

$=a^2+\frac{1}{a^2}+2$

$=27+2$

$=29$

Thus, $a+\frac{1}{a}=\pm \sqrt{29}$