Question

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

Answer 1

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

/* 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 */

$\Big( a + \frac{1}{a}\Big)^{2} = 6^{2}$

$\implies a^{2} + \big(\frac{1}{a}\big)^{2} + 2\times a \times \frac{1}{a} = 36$

$\implies a^{2} + \frac{1}{a^{2}}+ 2= 36$

$\implies a^{2} + \frac{1}{a^{2}} = 36 - 2$

$\implies a^{2} + \frac{1}{a^{2}} = 34$

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