26. If (a² - 4a - 1) = 0 and a ≠ 0, find the values of : (а²- 1/a²)
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Answered by
8
Answer:
± 8√5 (it means 8√5 and - 8√5)
Step-by-step explanation:
→ a² - 4a - 1 = 0
→ a² - 1 = 4a
→ a - (1/a) = 4 ... (1)
Square on both sides:
→ a² + (1/a)² - 2(a*1/a) = 16
→ a² + 1/a² = 16 + 2 = 18
Add 2(x*1/x) to both sides:
→ a² + 1/a² + 2(x*1/x) = 18 + 2(x*1/x)
→ (a + 1/a)² = 18 + 2 = 20
→ (a + 1/a) = ± √20 = ±√(4*5) = ±√(2² *5)
→ a + 1/a = ± 2√5
In question,
→ a² - 1/a²
→ a² - (1/a)² = (a + 1/a)(a - 1/a)
→ (± 2√5)(4)
→ ± 8√5
Answered by
2
Answer:
Step-by-step explanation:
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