Question

3. If a? – 4a - 1 = 0 and a = 0, find the values of:
(i) (a-1¹/a)

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Answer 1

Correct Question:-

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

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

I hope it's help with...☺