Question

(a+1/a)2-(a-1/a)2 simplify​

Answer 1

Answer:

$( { a + \frac{1}{a} )}^{2} - ( a - { \frac{1}{a} )}^{2} \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2 - {a}^{2} - \frac{1}{ {a}^{2} } + 2 \\ 2 + 2 = 4$

Answer 2

Given:

a, 1/a

To Find:

(a+1/a)2-(a-1/a)2

Solution:

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

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

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

$= 4$

The simplified value of (a+1/a)^2-(a-1/a)^2 is 4.