Question

5) if
$(a + \frac{1}{a} + 2)^{2} \: is \: 4$
then find
$a ^{2} + \frac{1}{ {a}^{2} }$
​

Answer 1

Solution :-

x² + 1/x² = 18

Adding 2 on both sides

⇒ x² + 1/x² + 2 = 18 + 2

⇒ x² + (1/x)² + 2(x)(1/) = 20

⇒ (x + 1/x)² = 20

⇒ x + 1/x = √20 = ± 2√5

x² + 1/x² = 18

Subtracting 2 on both sides

⇒ x² + 1/x² - 2 = 18 - 2

⇒ x² + (1/x)² - 2(x)(1/x) = 16

⇒ (x - 1/x)² = 16

⇒ x - 1/x = √16 = ± 4