If a -1/a=5 and a+1/a=6 then find a²+1/a²

1.	If a -1/a=5 and a+1/a=6 then find a²+1/a²
Answer» $1 ) If \: a - \frac{1}{a} = 5 \:--(1)$ /* On SQUARING both SIDES we GET / $\Big( a - \frac{1}{a}\Big)^{2} = 5^{2}$ $\implies a^{2} + \big(\frac{1}{a}\big)^{2} - 2\times a \times \frac{1}{a} = 25$ $\implies a^{2} + \frac{1}{a^{2}}- 2= 25$ $\implies a^{2} + \frac{1}{a^{2}} = 25 + 2$ $\implies a^{2} + \frac{1}{a^{2}} = 27$ $2 ) If \: a + \frac{1}{a} = 6 \:--(2)$ / On squaring both sides we get */ $\Big( a + \frac{1}{a}\Big)^{2} = 6^{2}$ $\implies a^{2} + \big(\frac{1}{a}\big)^{2} + 2\times a \times \frac{1}{a} = 36$ $\implies a^{2} + \frac{1}{a^{2}}+ 2= 36$ $\implies a^{2} + \frac{1}{a^{2}} = 36 - 2$ $\implies a^{2} + \frac{1}{a^{2}} = 34$ •••♪

Answer»

$1 ) If \: a - \frac{1}{a} = 5 \:--(1)$