Question

if a^2+1/a^2 = 47 then find the value of a+1/a

Answer 1

Answer:

$a + \frac{1}{a} = 7$

Step-by-step explanation:

$Given, \\ {a}^{2} + \frac{1}{ {a}^{2} } = 47 \\ Since, \\ {(a + \frac{1}{a} )}^{2} = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \\ = > {(a + \frac{1}{a} )}^{2} = 47 + 2 \\ = > {(a + \frac{1}{a}) }^{2} = 49 \\ = > a + \frac{1}{a} = \sqrt{49} \\ = > a + \frac{1}{a} = 7$