Question

If [x-1/x] = 8, find the values of (i) [x+1/x] (ii) [x²-1/x²].​

Answer 1

Answer:

2√17 & 16√17

Step-by-step explanation:

Square on both sides:

→ (x - 1/x)² = 8²

→ x² + 1/x² - 2(x*1/x) = 64

→ x² + 1/x² - 2(1) = 64

→ x² + 1/x² = 64 + 2 = 66

Add 2(x*1/x) to both sides:

→ x² + 1/x² + 2(x*1/x) = 66 + 2(x*1/x)

→ (x + 1/x)² = 66 + 2(1) = 68

→ x + 1/x = √68 = √(2² * 17) = 2√17

Therefore,

→ (x)² - (1/x²)

→ (x + 1/x)(x - 1/x)

→ (2√17)(8)

→ 16√17

Answer 2

Answer:

1)Given , X-1/X = 8 after Squaring we can find X+1/X = 2√17 so the answer is 2√17

2) similarly if we have X-1/X = 8 then we can easily get X²-1/X² = 16√17.