If a2-1-a2 - 23- then the value of a-1-a is equal to -

Using the identity, (a+b)^2 = a^2 +b^2 +2ab, (a+1/a)^2 = nbsp;a^2+1/a^2 + 2 nbsp; ⇒(a+1/a)^2 = 23 + 2 nbsp; ⇒(a+1/a)^2 nbsp; = 25 ⇒(a+1/a) nbsp; = ± ...

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Standard XII

Chemistry

Heat Capacity

If a2+1/a2 = ...

Question

If $a^{2} + \frac{1}{a^{2}}$ = 23, then the value of $a + \frac{1}{a}$ is equal to .

\pm 5

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Solution

The correct option is A $\pm 5$
Using the identity,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$ ,

$(a + \frac{1}{a})^{2}$ = $a^{2} + \frac{1}{a^{2}}$ + 2
$\Rightarrow$ $(a + \frac{1}{a})^{2}$ = 23 + 2
$\Rightarrow$ $(a + \frac{1}{a})^{2}$ = 25
$\Rightarrow$ $(a + \frac{1}{a})$ = $\pm 5$

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If a2+1a2 = 23, then the value of a+1a is equal to .

The correct option is A ±5Using the identity, (a+b)2=a2+b2+2ab, (a+1a)2 = a2+1a2 + 2 ⇒(a+1a)2 = 23 + 2 ⇒(a+1a)2 = 25 ⇒(a+1a) = ±5

If $a^{2} + \frac{1}{a^{2}}$ = 23, then the value of $a + \frac{1}{a}$ is equal to .

The correct option is A $\pm 5$
Using the identity,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$ ,

$(a + \frac{1}{a})^{2}$ = $a^{2} + \frac{1}{a^{2}}$ + 2
$\Rightarrow$ $(a + \frac{1}{a})^{2}$ = 23 + 2
$\Rightarrow$ $(a + \frac{1}{a})^{2}$ = 25
$\Rightarrow$ $(a + \frac{1}{a})$ = $\pm 5$