Question

If a-1/a=3 find a^2+3a+1/a^2-3/a

Answer 1

$Given \: a - \frac{1}{a} = 3 \: --- (1)$

$\red{ Value \: of \: a^{2} + 3a + \frac{1}{a^{2}} - \frac{3}{a}}$

$= a^{2} + \frac{1}{a^{2}} + 3a - \frac{3}{a}$

$= \Big( a - \frac{1}{a} \Big)^{2} + 2 \times a \times \frac{1}{a}+ 3\Big(a - \frac{1}{a}\Big)$

$= \Big( a - \frac{1}{a} \Big)^{2} + 2 + 3\Big(a - \frac{1}{a}\Big)$

$= 3^{2} + 2 + 3\times 3\\= 9 + 2 + 9 \\= 20$

Therefore.,

$\red{ Value \: of \: a^{2} + 3a + \frac{1}{a^{2}} - \frac{3}{a}} \green { = 20}$

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