Question

If a- 1/a = 3 then a2 - 1/a2 =

Answer 1

$\large{\red{\underline{\underline{\bold{Given}}}}}$

• a - 1 / a = 3

$\large{\blue{\underline{\underline{\bold{To Find}}}}}$

• Correct question a² - 1 / a² when the value of a + 1 / a = 3

$\large{\green{\underline{\underline{\bold{Solution}}}}}$

a - 1 / a = 3 , a² + 1 / a² = ?

As we know that ,

a² + 1 / a²- 2 a × 1 / a = [a - 1 / a]²

[a - 1 / a]² = a² + 1 / a² -2 × a × 1 / a

[ 3 ]²= a² + 1 / a² -2

9= a² + 1 / a² - 2

9 + 2 =a² + 1 / a²

a² + 1 / a² = 11

Answer 2

Answer:

$\frac{a - 1}{a} = 3.....(i) \: \: \: \: \: \: \: \: \: (sq.both \: side)$

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

$a ^{2} + \frac{1}{a ^{2} } - 2 \times a \times \frac{1}{a} = 9$

${a}^{2} + \frac{1}{a^2} - 2 = 9$

${a}^{2} + \frac{1}{a ^{2} } = 11$

now adding 2 on both the side

$( {a}^{2} + \frac{1}{a ^{2} } + 2) = 11 + 2$

$(a + \frac{1}{a} ) ^{2} = 13$

$a + \frac{1}{a} = \sqrt{13} ....(ii) </p><p></p><p>from equetion (i) and (ii) </p><p>$

$(a - \frac{1}{a} )(a + \frac{1}{a} ) = 3 \times \sqrt{13}$

$a ^{2} - \frac{1}{a ^{2} } = 3 \sqrt{13}$

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