Question

If a²+1/a² = 34, then the value of (a +1/a ) is -----
±7
±6
±2
±3

Answer 1

Answer:

a²+(1/a²) =34. {a²+b²}

a²+(1/a²) +2=34+2. {a²+b²+2ab)

(a+1/a)²=36. (a+b)²

(a+1/a) =√36

a+1/a=±6

±6 is the answer

Answer 2

$Given \: a^{2} + \frac{1}{a^{2}} = 34 \: --(1)$

/* Add bothsides of the equation by 2, we get */

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

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

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

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

$\implies \Big( a + \frac{1}{a}\Big) = \pm 6$

Therefore.,

$\red{Value \:of \: \Big( a + \frac{1}{a}\Big)}\green { = \pm 6}$

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