Question

26. If (a² - 4a - 1) = 0 and a ≠ 0, find the values of : (а+1/a)​

Answer 1

Answer:

Your answer is 1 + root 5/2 + root 5

Answer 2

Answer:

± 2√5

Step-by-step explanation:

→ a² - 4a - 1 = 0

→ a² - 1 = 4a

→ (a² - 1)/a = 4

→ (a²/a) - (1 /a) = 4

→ a - (1/a) = 4

Square on both sides:

→(a- 1/a)² = 4²

→ a² + (1/a)² - 2(a*1/a) = 16

→ a² + (1/a)² - 2 = 16

→ a² + (1/a)² = 18

Adding 2 to both sides:

→ a² + (1/a)² + 2 = 18 + 2

→ a² + (1/a)² + 2(x*1/x) = 20

→ (a + 1/a)² = 20

→ a + 1/a = ±√20 = ± √(4*5) = ±√(2² *5)

→ a+ (1/a) = ± 2√5